The Young Surveyor's Guide: Or, A New Introduction to the Whole Art of ...

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- '^'T" ^

THE ^

Young Surveyor's Guide

O B, A

New INTRODUCTIOI

TO THE'T:

Whole An of Surveying Land^f,

Both by the CHAIN and all:
Inftruments now in UCe.

Now fr^ PubliJFdfrom an Origtnd M. S.
To which is Added,
All the ufefiil Qeometrical Defnhiom, Axioms,
PioilemsmA Thearemr, which reUre ro this Arc. As
alfo theMeihod of Calling up the Dimenfmns of Ar-
tificers Work. Very ufirful tor all GcDtlcmca and
Otheri-
There is alfo added, ty way of APPENDIX,

a new way ot Surveying large Trafts of Land, ac-
cording to the Leirned Mr Wbifton's aad Mr D'ltton't

New Method of Surveying EngiauJ by Exphfnnt.

The manner ot malting up and preparing
Tranfpatenc Colours for Beautifying Maps, Charts,
Piaures, ify-c.

The Tables of Artificial Numliers, Sines and

TangeDts,[o every Dcgrn^andMiDUteohheC^jadranc.
All which U very much Improved and Corrected,

By EVJrARD LAURENCE,Satveror.

LCWDON, pTintd far James KnaptOD, at the Cro«»
in St P,iul's Churcb-Tard. 1 7 16.

4/^

Hes

,t3r

73M^

J-

THE

J PREFACE

ALT HO' . there is' little need
of faying any tbin^ jrj, way of
Preface to the faSoiving Trea-
ttfe ; yet Cujloni having made

■ rC almoft as niceffary ai an Entrances to
an Houfe ; IjbaO fo far comply with

, Cufiom as to fay^ That the following Di-
\ regions for Surveyings die. were put into

■ fry Hands in M. S. to be Enlarged, Cor-
reSied and Improved^ in fuch a Manner '
as to make them of General XI fe and
Maf^ fraBice^ according to the modern^
Befi, and mofl Improved Methods m
that Excellent and TJfeful Science,

HoTV far and htnv well that De/ign-
and Purpofe hath been purfued in the-
following Fages^ I muft leave to the In- ^
genuous Reader to judge, after I have-
jufi told him that H* wilt meet meet
A a- ttfith'

The Preface.

with feveral very ufeful Definitions,
Axioms, Problems am Theorems, wbol-
Ij new, or at leafi newly applfd. Here
will he found alfo feveral new Problems
added, relating to the Art of Dividing
Land., As alfo a Neiv Method of Sur-
veying large TraSs of Land, hy Sounds as
well as ^igbt, hyVertue ofdiftant Explofi-
ons^ fir {I Invented and Publifl^ed by thofe
two great Genius's and Improvers of Na-
tural Hhilofoph)i,tbe Learned Mr Whjfton
and Mr Ditton.

I jhall only add^ That to make this
Treatife of as General Vfe a^ may be,
the Reader will meet with an ufeful
ColleEiion of all tranfparent Colours pro-
■ per for the Beautifying Maps, Charts^
&CC. . which perhaps may be thought
entertaining to the Curious. But if I have
made the whole Eafy, Natural and In-
JiruHive, I have gained my End^ and the
SadsfaSion I aim at*

Edvard Laurence. ]
CON-

«

CONTENTS.

GEomettical Dfinitions, Pdg. i

Maxivu. 5

Probkmu 10

Tbeoremt. ig

Drfmtiom of Right Lket appl/d to a Circle. 30
Plane Ti i^onometrj. a 2

PraSical F. igonometrj. .f?

LeveSittgof Ground: jg

Ke I^e cfiie iW 0/ Namhsrt. 62

Meafuring. _ ^3

Meajmirg Jrt'rji.ers Worh 4,8

Sarveywg ef L<ati ly the Ch^in. aj

Surveying of Ljtrd by the fhrie Table. 1 p i
Sill vejh^^ the Theodolite or Semicircle. 1 y3
DiviiliiTg of Landt. loy

SeJucivg Statute Meafure to Cvflomary Mea-
fare. ,^3

Laying out A^iP Lmds, ig^

keduiit^ rf Plots. 1 j, g

APPENDIX.

Taliiig the Gtomd-fhtof a Cty or Corpora-
tioH. ,^l

A new iigthod of Sutvcyirg a Qmtry or Ivge
TraSs of Land. 2iQ.

FrepJti^ Cohwt for Wa^ivg Maps. 7\6

The

The Explication of the Signs and
Charafters ufed in "the Treatife^

'EguaUtj, or eqnal. to.

Majority^ orgrtater than.

Mhttritji, or lejftr tbiaii

Morfy or to be aided.

Left, or to befubfiraSei. .

Anfjti vffd in Trigonometry,

Therefore.

Pfoportjon,
•Jt^U nfed m tht Tbeoremu

errata:

PAG a. l'nieiS,pmi Teriod afteritp. 4.^?,dcIe•-
B.^ 5./. 34„r. dividing it.^ 6./. aj.forthefe.r.
rwo.>7. /. a8, r. preeede-p. 8. (.ai, for another, r.'one
Point. ^ 9. /. 18, r. Oftahedron.p. p./. as,)-. Icofahe-
dron. p. iz.'.ii, r.aLiDi.p.i4.I.9,for whoft iidc),
r. each fide whereof, p. 16./. 17, for are, r. is. ^ 19./.
13, r. Angles. >. so. /. 23, r.falling.p. 21. i- i, r. per..
jd Dcf. p. ax./. II, r. i7thDef. p.as-^- =', r. 13th
Dd. p. 38. /. aj, r. i,thDef. p. 29. 1. IJ. for may, r.
wii. p. 31. /. 10. inflcad of f or, r. from. p. 3d./. 3, for
68. (Si. r. 168. tfi.p. 37. /. ij, for 52—30, r. ai°3o'
p. 39. /. 8,.r^ 407.6. p. 3J.I a, r. Triwglc for Angle,
p; 39./. It, r. Acucc Angle b. p. 40./. to, for b, r. bd.
^4I./. II, foiab, r. cb. p. 41. i. 16, forjOiUir 39*
aa'p. 4ii. 1.17, ford,r.da.p, 45. /. a, for 639 r. 6,3.9.
p.5't. /. a9, dele and. p, 53. /. ii,fordt', 8a', r. 51°^
Ji'. p. 5J. /. as, forfir, 8x', r. fii", ja'. p. S4.J. x5,
r. 7i:,a5'. p. 57, /. 17, r. Marks, f . tfo. /. ad, r. he-
wixi the Quancr. p. 6^.1. &4,r. meacioncd.p. 71./. igj
r. It is. p. 73./. 19, for Br. 8. p. 88. f. s6, for 29, r.
Sf p. 8 9./. 9. and 11, fortf, r 4. p. 9S9 /. a, put the
Word UcduftioDa over the two Right-hand CoJumns p».
99-'. ij.r. i98irftcadof jy.p. I03./. 17. and 18, for-
Rod, r, Rood./. 104./. 19, for Roots, r Roods p. 108;
t. afi, tor Circumfercice,r. Circumlerenror. p. 1 ij, /.
li, r. pJacinj. p. 127.; i4,r. fi£. pi. p. 166. 1. 9,
•r Arc, r. Arc of a Circle, p. 167. /. is, r. Circuoi^-
ft!Tentor,.p. 169. /- ii,/or ,Ji r.-^fj. ;. 185, /. 12,,,
A-cicbcr of the Product it.

ADVERTISEMENT.

LOrdftiips Surveyed, and Maps drawn
of the fame. Timber Meafured
and Valued , with other Artificers
Work i and Dialling in all its Parts,
Performed by Edward Laurence^

He is to be heard of when in Lon-
don at Mr Senexs at the Globe in
Salisbury-Court.

K K In Winter, and at fucK
Times as he is not Surveying, Gen-
tlemen may have their Sons or
Daughters Taught Accompts after
a Natural, E^fy and Concife Me-
thjid^ with the Ufe of the Globes and
Maps, and all other ufeful Parts of
the Mathematicks.

/ .\-

XT

-^

THE

k Young Surveyors

[guide:

L Pradrcal Geometry.

F 'WF' Defign in this part to lay down tfie

I firft Principles of Geometry ; and to

f ■ do it metnodically, to b«gin with

^' ■ Xefinidons, and the Eiplication of

W J^m- *^^ moR ordinary Ternrs : To wbich

^ I fliall add . fome Maximsj wherein Natur^

[ Reafon does inflnifltM; andjhen proceed

■^ 10 Geometrical Problems j and fuch Proixp-

K iitiom as I And convenient for (his Tra^

■ fo'that a Man may be able to give a de-.

inooflrable Account of what he does.

a The Toung Surveyor's Guide,
Geometrical Definitions,

1 A Point is that which is confidered ar
^avi^gno manner of Dimenfions: And as
being indivisible in eve*y refpefl, the Ends
or Eltiemities of Lines are Points.,

2 Fig.i A Line hasLensth, IwrnoBreadtb^
not Tbickneff $ of which there ire two forts,
lis. right or ftreighf, snd curve or crooked j
as AB i!s a flreight Line, BC a crooked
Line.

3. Fig. 2. An Angle is the meeting of two
Lines in a Point; provided the, two Linn
fo meeting, do not make one flreight Line:
As in the tines AB and AC nvcting to-
gether in the Poijit A, make .an Angle.
BAC, which is meafur'd by an Arch of a
Circle E)E,deftribed from the angular Point
A as a Center , and intercepted between
the Lines AC, -and AB, which form it an
J«gh^ is faid to be equal to, gweater arUft
than another, according as the Arch which
iiteafijres ir, contains zsmtny, taore, erfeair
of the equal Paits into which that Qrcam-
ference is furpfed rofeedirtded.

Of which right-lined Angles there are
three forts, Dial" Right Angled, Acute, and
Obtufe: vf,htn a Line faHeth perpendicularlj
upon another, it makeih two right Anglee,
th»t is, neither Ifsnetb to oa» iide or the
other.

Ex^mpk.

The Tefung Sfirvejf<ir*s Guide. $ |
Example, i

ffg. 3. Let CAB be a right Line, DA per-
pendicular to it, that is to faj, neither lean-
aog towards B or C, but eiaflily upright,
then are boih the Angles 9t A, vi-^. IjaB
and DAC right Angles, and contain in
eadi juft 90 Degrcfs, or the 4th part of a
Circle ; but it the Line DA had not been ^
Perpendicular, biit bad leaned towards B,
-then bad DaC been an 'Obtufe Angle,
or greater then a right Angle ; and DAB,
an Acute Ar^Uj or kfs ihen aRigbt Angle.

4.AFigure is that which is comprehended
under one, or more Lims.

f.Al] Figures containedjunder three Sides,'
are c^Ied Triangles, which Euclid divides,
with refpfd either to ib^ir Angles or Sides.

£. Fig, 4. An Equilateral Triangle .is tbaQ
which hath ii8 three Sides equal, as the Tri-
angle ABC.

'J.fjgi. AnlfofcelesTrianglejis that which
hath two Sides equal: As if the two Sides
■ AB and AC be equal , the Triangle ABC
is Kcofcelefl.

8. Pig. 6. A Scelenum^is a Triangle having
all the three Sirfes nnfqual^as GHr

9. ¥Jg. 7. A Rcflarg^led Triangle, is tljau
which halb one right Angle, ae DEF.

10. P^',S. An Ambligone, or obnife Angled
Triangle, is that which hath one Obtufe An-
gle, HailGH. 3 2 Pit^

.4 . The Toung Surveyor*! Guide,

'* ^ • f''&- 9' An Oiygone, or Aaite Angled
Triangle, it that whofe Angles are all
- Arutp, as ABC.

1 7, Fig lo. AS^uareconftJls offoar equal
Sides, ;ind four right Anglei, as AB.

1 7. A Paranelogram is a Figure that
ha'li its two oppofite Sides B parallel.

i4.P/;g.n. AnOblongRedangle,having, ifs
oppolite Sides e(|ii«l, and its Aogles tight^ a«
CB, is railed a long Square or Parallelogram.
1 5. fig. 1 2. A Rhomfcus,is that whofe Sides
are all t^ual, but not right Angled, as B.
, 1 6. tig. 1 1. ARhoinboideSjis that whofe op-
.pofite Sides and Angles ar^ equal among
thcmfelves ; but not right Angled, as D..

1 7. Fig I -c.Paral lei Lines are fiich as being in
(he fame Plain will never meet, keeping ftill
(he fame diOance one from the other ; as
AB and CD

I &. Fig. I ;. All oiher four (ided Figures are
railed Trapezia: Other Figures that are
contained under 5, 6, 7, or more Sdes, I
cirlt Irregular, I'olygoneB, as F is an Irre-'
gul^r Figure, and G is a Trapezia.

Kote^ Such as are made by the Circum-
ference of a Circle divided into any Nutfi-
i>er of eq'ial parts , are regular Figures 5
having alt their Si^es and Angles cgnaJ,
and are called froni the Number of Angles
they conrain, as a Pentagutie, Hexagove, Hep<.
fiigotie, OSagotie^ &c. Which fignifits a Figure
,Dt 5, 6, 7 or 3 Angles or Sides, whofe
■ S.d«

The Toung Survej^or's Guide. 5 '

Sides and Angles are all equal one to an-
oJher; Fer your better underftailding of '
which, obferve the Figures lollott'ing.

19. Pfg- 16.N0W fappoiing the Sides and -
Angles robe all equal, (A) is a regular P«(--
gane^ (B) a H^x^gone^ and G a Heptagons, Sec.

20. Fig. 1 7. ACircle is a plain Figure, con-
tained under one Line only, BDCGE, which
is called the Pert>phery,in the Middle where-
of there is a point A, which is called the
Center j from whence all right Lines that
are drawn to the Circumference are c-
qual i ai AB, AC, AD. ■

21. The Diameter of a Circle isa rjghe
Lina drawn through the Center, and tpr-
minated by the Circumference of theCif--
clej thereby dividing it into rwo equ:il'
parts.

22. F;^. 1 7.The Semi-diameter or Radius is*
the halt of the whoL' Diameter; as AC or '
AB are Semi-diameters.

2j. A Chord is 3 flreight Line fiibteiidln^T'
in ,Arch of a Circle, dividing into two
parts.

24.^)^.17. ASemicircle is the half of aCir-
cle, contained under the Diameter and half '
Peiiphery, as DBC or EEC.

25, Fig. 17. A Quadrant is one fourth part
ol a Circle; and is made by the interfedti-'
on of two- Diamiiers perpendicularly, as.
ADC or ABD.

B. 3 26. Fi^:

^:

^ Tbs Toung Surveyor'r Guide*

26. Fig. 17. A Segment ii aFigure compre-
hended under psrt of theQfcumference of a^
Circle, and the Chord belonging 10 it, as
ECG, by the Chord Line EC.

27. J^/i?i7,ASe£torof aCircleisaFignre
contained under two Right Lines, drawn '
irom the Center A, and rhe Circom-
ference lying between the fame Linea, as
ABD.

23. All Circuroferences,ai alfo like Archep,
Sines, Tangents, Chords and Secants', are
roportional to their Radiif That Wy if the
.adius of one Circle be double, treble, &c,
the Radius of another : TheCircumference as
alfo likeArche£(i.e. containing the (zmt nom-
ber of degrees,) aod (heir Sinet, Tangent*,
Cliords, &c. of the former will be double,
treble, Cfc. the Circumference like Arches, -
iheir Sines, Tangents, (fc.

29. fig. 19. A Diagonal is aflreif^ht Line
^rawn from one Angle of any Figare, to-
ihe oppoCte Angle, asCAfi,

MATIMS*

1. Thofe Qjiiantities that are equal t»
third, are equal betwixt themfelves.

2. If egualQaantitiesbe added to thofe
that are equal, the Sums will alfo be e^oal.

3. If equal Qpantkies be taken away from '
thofe that are equal, the Remainden will .
be equal.

If

The Toung Surveyor's Gui^e, 7

' 4. If yoa add equal Qpantides to onequal,
fae whole win be unequal.
' 5. If from equal Quantities you take un-
'qtial, the Remainder will be unequal.
' ^. QuaQtities that arc double, triple, qux-
Iruble Cc. to the fame Quantityj are equal
imong themielves.

7. Thofe things which mutally agree to
nch other, are equal.
: 8. Right Anglts are equal to one another.

9. Parallel Lines have a common Per-
pendicular.

JDVE rtissment:

Thtte are two forti of Propofitiom, vis.
problems and Theorenn. A Problem always '
{iropofes fomething to be done: But a The-
orem is a fpeculative PmpoArion, in which
Rre confidered the AfTedions add Fropei?
ties of things already done.

Of Proportim.
Multiplied Magnitude, is that w^ich ror -
tains another Maguittide, a certain Number
of times [weciftfly.

Ratio or ReafoD, is the Comparifon of
two Quantities one with another, wheisby
one is faid to be bigger or lets than an-
other; in which Comparifon, that whith
proceeds, is called the Antecedent, and the
other the OmfequcBt. ' .

,■ - B 4 Thofe

S The Toung Surveyor'^ GuiJiu

Thore QiuDtitiet onljr admit of Reafbn*

which being maldplied may exceed eac^

other.

10 TheHomologusTerm* in anyProporti*

on are the two- Antecedents-, or the two

Confeqiients.

Reciprocal Figtires, are fuch is are when

we compare the Sides of one Figore to the

Sides of the other, and the Antecedentf,

and the -Confequents of the Reafoni ara ia

both Figures.

Of SoUis^va.. SoJidBediet.

A Solid Angle, is made by the meet-
M^g together of feveral plain Angles in
one point, ami of tbe& there mun be 3
at lead.

Like redilineal fblid Figures, »'e fueh
as are contained under an equal Number
cf like Plains.

A Pyramid is a folid Figure , contained
tinder Plains colleded from one Plain
to another.

A Sphere is a fblid Figure, bounded with
a Surface, to which Supenicies all the flreight
Lines that cm be drawn from the Center
are equal.

The Axis of a Sphere is 3 rightLine drawn
through the Center to both parts of the
Circumference, about which, if a Ssmi-circle
be tum'd, it will beget a Sphere,

The Toung Surveyor's GuiJei 9

A Cone is a foHd Figure , arifing
" from a arcuW Bafe of Breight Lines, end-
ing in aPoiiit called the, Vertei, or top
thereof; and the Axis of this Ccne, is a
right Line drawn from the Veitei to the
Center of the Bafe , and is called a right
Cone, -if the Alis be perpendicular to.
the Bafe, if- noF^ a Sca!en« one^

A Cylinder is a MiiA Figure, rifing fronr
a circular B:ife as the Cone dofs ; but the
right Line end all in ao equal Circle.

A Cube is a Solid Figure contained un-
der 6 equal Squares.

A Tetrahedron, is a (olid Figure com-
prehended under 4 eqjal and equilateral
Triangles 5 fo that its Bafe is equal to
each fide.

An O^atredron is- a folid Figure contair.-
ed under 8 equal and Equilateral Triangles.^
'-■Ihii. Dodecahedron, is a folid Figure
contained under 12 equal equiangular and-
Equilateral Pentagons.

Tht Icofiedron, is. a folid Figure con-
rained under 20 equal and equihterat
Triangles. •

Befides thefe five regular Bodies, it's
iinpoflibleio find any others, i. e to form
any more regular Bodies than ihefe hft,
wz. three are made tA Trianglfs, one ot
Squares, and one of Pentagons.

%% BaSicat

lo 7he Toun^ Survty9r*s Guidt,

Tra&icd Geometry,

I PROBLEM. I.

J?f. "T* O tftGt a Perpendicular J from
so. X ih« Point B on the Line KN.
Open jour CompilTe* to any faiall di-
iiance { fet one Foot in B, and wiih tlit
other makft the 2 Maiki D, G. (his done,
open the Compafles to any auiveotent
diflancp, then fet one Foot in D, and
with the other draw the obfcuic Arch
GG.

Again, theCompafles flill keesii^the fame
tliAance, fet one Foot in the Point <^ and
defcribe the Arch HH, crofling ihe ter-
mer in the Pouit A« from which draw
the Line AB, and it will bt perpendi-
cular to the given Line KN.

PROBLEM, U.

Jv^.ZT.To raife a Perpendicular DBtttpon
the End of (he Line AB. Open your Com-
■piffft to any ordinary extent, and fetli^
nne Foot upon the point B, Itt the other
fall at plealure, as at the . Point K, and
. without Bltering the Compa£res, fet oiM
Foot in the Point K, and witli the olher
aofs the Line AB, at D, alfo on the othw

The Tottng Surveyer*! Gwdc. 1 1
Side defaibe the Arch EE, then, lay your
Ruler to D, and K, drtw the Line DKF:
lallly, from the poim B ro the Inteifeaion
at g, draw the Line BgD, which it pec-
peodtcalar to the Line A^

PROBLEM III.

F!g.22,'Vo let/all aPeTpendicuIarA£,to tite
^ivea Line. RQ,/com the givenPointA^u'hich
18 oat of the Line BC i having fet the loot
of the Compailes upon A, with any Inter-
val, defcribe the Arch BC, which will
cat the Line RQ, at the points Band O
Then divide the Line BC into two equal
parts at the point E. I fay the Line AE
is perpendicular to RQ.

PROBLEM IV.

J^. 2^ From apoint C given i to draw a
Line CD Parallel to the Line AB given.

.On the Point C ai on a Center, ftr ike anArch
of s Circle cutting the Line AB given in
the Point A : Then fet the Foot of the
CompafTes any where (at a good Jtfimce

from A) in. the given Line AB, as B, and
with the fame Interval ftrike the Arch D :

-Then take in the CompafUs the Length

.AB, and. putiag one Foot in C, draw id
Arch cutting the other in. the Poinf D,
through C and D,' draw the Line CD,
and it will be parallel to AB. PfiOS.

r

t3 The Toung Sitrv£jror*'s Guide*

PROB^LBM y.

Ftg. 24. To dividfl the given nght Line
AB into two ttpal parts, and at Righl
Angles. Take in your CompafTo any di-
llance above half the length of the Lin«
AB, and felting one Foot in the end A,
with the plher draw the A'ch CDE, then
with the fame interval on theGenterB.defcribe
the Arch FGK, intercepting the former in
F and G, from which Points draw the Lin*
FGH, aod it ii done.

PROBLEM VI.

A fecond way to draw Lines Farallt4
to each other.

Fig. 2 ; . Let- BD he a Line given j to make
a Line Parjilel imioit, fet one Foot of
ihe CompiflVs at G, and: with the other
defcribe an Arch as a e, and do the faine
at: the other end of the Line, and through
the uimcfl Convciity, and of thofe two A^
ehes diaur the Line IL.

PROBLEM- Vir.

A third way how to draw Linei Pa-
sallel to another Line, which alfo paiTis
IJMOugh a PoMit afiigned;

. Go.HjIc

-7he Toung Surveyor's Guide, j^
H^. 26. Let BD bathe given Line, E, the
Point through u^ch the Parallel muft pafti
Place one foot of your Compares In £, and
open them till (he other foot juft touch the
X'ne BC, and defcdbe (he Archd^j with
the fame extent in zay part of the given
Line, fet one foot of' your CompaHet, and
ftrike the Arch D, then tlirengh the poioS
E and the utmofl Conveiity of the laft Arch
draw the line CK, which ii parallel to BD
aiid through the point E.

PROBLEM yill .

^:^.27 Todeftribea Tiiangle.ACB^wKofe
fides, AC, CB, and AB,fhall be equal to the
three tides, E, D, and F given, provided
that any two of thepi be greater than the
third. Take with your Comfiafrei the Line
F, fo which make AB equal : Then on the
Center B- with the diflance t) defcribe the
Arch z X. Again on A with the Line E def'
rrifae an Arch cotfing the former in C, theii,
draw AC, and CB, and it is done.

PROBLEM IX.

. Kote^ The very fame way yot] mrty
make a Triangle e^al to anoibcr Triangle .

14 Tht Toung Surveyor's Guide^
PSOBLBM X.

Fig. 2%. To make anAogleBACequ'Ito the
AagleEDFat A the end o(the Line ABgtven.
Defcribe from the Poiota A lad D as Ceo-
ters two Arches BC, and EF, with the (ame
inrerval of the Compaflrij then take the
diflance EF, and fet it fromB to C, then
draw the Liae AC, I /ay, the Angles BAG,
and EDF, are equal.

PROBLEM XI.

F^. 39.T0 make a Square BCDE, whofe
^ea Ihou'd be eqnal to die given Lice A :
Fiifl, make the Lice EC,e()ual to the Line A,
and on the end thereof at C, ered the Feipeo-
dicnlarCD alio equal to theLine A,then with
the fame diftance, fet one foot in B, flrike
the Asch k i, and on D defcribe the Arch ^,
cTofling each other in the point M, which
will confiitute the Square BCDE;

PROBLEM Xn.

J^g. 30 To make a ParallelogramABCDor
long Square, having one fide equal to A and
the other to B. This ia like theiormer; let
two Lines be given you, ,AB and BQ and
let it be Keqmred to make a Parallelogram
oi tbmn. Fiift lay down youi Idngeli fide

The Toung Surveyor* s Guide, 15
AB «qual to A, and at the end ere£t a p«r-
pendicular Line equal to yout fitorteft Line
EC, and fo proceed , as you were taught u
the laft Problem.

PROBLEM XIII.

J^. 31. To inalcc a Rhombus ABCD.

Make an Angle, as ABC, and make the
fides AB, BC equal, then taking the length-
of one of them and fetting your Compafft*
in A, defcnbe the Arch m m j alfo put one
FootinCandftrike the ArchnifXaniydraw
the Liqes DC and D ^ and it's finilhed.

Nae^ A Rhombus is made by 2 equila.-
teral 01 Ifofceles Triangles.

PROBLEM XIV.

i*^. 3 2. To make a Trapeziam. A B C D,

which Ihall have one Angle at C egiu) to.
a'giren ApgleE.andthe four fides equal to
foor given Lmes, vrc th« Lines f g h i.

Fig. 52. FirJ^ Make the Line AB equal to
one of the given Lines, as f. 2dly. Upon the
point B,(by Prob. 10.) make the Jungle ABC
equal to the Angle E , makirg the fide CS
equal to the given Line g. jJ/jf, Take another
of your given liijes, as the lineh, ,andfet-
tirg one Foot upon C, wiih the other defcribe
, the rtrch b b. taftly., Take the fpurth line j
in your Camsa^es, (ctting; one foot in \
with

i6 The Toun£ Surv^or'f Cnide*
with the other defcribe the Arch o o, and
draw the lines DA and'DC, which will con-
fttute a Trapeziana, the fides whereof are
equal to the four lines given, and it has an
Angle equal to the Angle gtren,, which was
to be done.

PROBLEM XV.

K^ 33.T0 divide a Circle ABCD,:n(oanjr
Number of equal [jarts, not exceedirg Ten.
Pirft^ D'fcribea Circle, and crofs it with 2
Diameters, AC and BD, pafling through
the point or Center E, and make A o and A
Cfc equal to BE, and join OQ 5 To is OQ, the
third part of the Circle: then join AB toge-
fh«r, fo will AB be the fourth partj upon L,
and thediflaTice LB, defcribe the Arch Bm,
and join Bm, which line is the 5th part; A£
or BE is the fixth part, and LO or LQ. are
thefevsnth pirt, and k A, will be the •ighih
part. Divide the Arch QAO into 3 equal
parts at S, and join SQ,, which will be the -
ninth part, EM is the tenth part.

So you may jnike the Figures railed"'
Ptvtagon^ Hexagon, Heyt^on, OUogon, iVwfu-'
gotf, !tc.

PROBLE M XVr.

Fig 34- Any three points A. B, and C, wliich
ace not is a ftreigbt L^ne, beinggiven j bow

Tb^Toung Surveyor J. Guide. 17
tcrfind the Center Oof the Cirrle BAC*
which fhall pafs thrpueh tbofe three givm
Poiots. firpj Set'one foot of the Compaflei
in one of the giren poiots, as in A, and ex-
tend the other foot to B,another of theppinlSj
and draw the Arch of a circle GFD.-^
Second^, TheCompaifes not altered, fet one
foof m B, and with the other crofs the foi*
mer Afch with two finall Archei in. the
points D and £, and draw the right Line
DE,— Tbirdfy, Set oneibotof the Com-
pafles in the ^d point C i they ftill keeping
the ^me diflance, and with the other foot
crofs the firfl drawn Arch GFD , in tht
points F and G, and draw the right Line
FG, crafnng the former right line DE, in
the pwnt Gs fo is O the Center fought forj.
upon which if you defctibe a Circle at the .
diftance GA, it fhall pafs through all the }
given points AB, arid C, as was required.

PROBLEM XVII.

How to make an Oval feveral ways.

Ftg 3 5. Make thretCircles whofe Diameters
-may be in a ftreight Line, as B : Crofs' the'
line with another Ft^rpendicuUr to it at the
center of the middleCirclev as cd \ draw the
lines ce, ch, dg, dfj fet one Foot of the
CompalTes in D, and extend the other to g,
defcribe theArch gf, with the fame eztent^fet-
ting one foot in c, dcfaibe the other part b e,
(hen

1 8 The Voting Surveyor't Gwde.

then frotntheCenter 0,wiihthedtftanceBO,
defcribe ihe Arch f BE. Again, with the fame
difiance on the Centtr Q_ Maibt the Arch
£AH, Bad it is donp. , . *

THEOREM I.

K^gtf.lfsny Triangle QRajith two fides,
QR, anri QS, egwl ib'.two Mttn qr, and
qs, in any other TffioRln, ^ct if dlfo the <
Q. included hy tliofe fides = to < q, inclu-
ded by the other fides i ^ fajr, each parr in
one Triangle is = to its correfponding pari
in the othtr,and therefore the whple Triangle
QRS ii = the Triangle qrs.

Demon. Foe fn^rafe the. Triangle qrs
l)e placed upon the A QRS, the fide qr will
fall exa^Iy on Q.R ( by thefeventh Maxim )
Knd the fide qs will fall on its equal QSibc-
caufi < Q. = < q fo the point S wjll fall
on s, and R onT,and therefore the'^ whoIeTri-
angles, q r s and Q)tS do murally agree, and
confequently each pait in cne is equal to its
corre^ndiDg one in the other.

ScboUum to thefrfi Prop.

By the fame Reafoning we may Djmon-
firate the following Theorem. >

If the fides R S, afid rsof the twd

Triangle 8 (^S, q r s were equal, and the <s

adJRceni

iff-'

7

^

^

^

-i-i,

\

1

g

7Be Toun^ Sarve^or*s Guide, i ^

adj-a«nt to thofe fides in the a Q^RS — to
•he <8 correfponding to them in the Triangle
qrs", all the reft, and alfo die TiianBlis them-
ftlres, will he equal.

For if the fide q r be put upon the fide '
QRjthey will agree {by Maxim "j.) but K-
«auie the < R = < r, and < S = <Si the
iide Rq will fill! upon fide RQ., and qs upon
OS, /. the point q will fall upon the pointQ,t
(j9T if it fail cut of ^ the hints r j, JJ do not
fall vpm the Likes ^, ^) therefore thtjt
aie equal (by tbefevaab Maxim) QZ D.

THEOREM lU

T&.37. fe «n Ifoceles TriangletheAigle at
the mfe oppofite to die equal Legs , are
equal.

tet tfie Triangle A C B be ruppofed
two Trianglei, and the Situation pf one cod*
ven to that of the other, asi c a; B^catife in
the two Triangles ACS and b cm, ^e fide
AC is = the fide b c, and the fide CB is =
the fide ab, and the Angle C is ^ the Angle
c, therefoH the Angle at the Bafe A = < b
by the firJl, which was to be Demonfirated
for the Angle, B and b are tite &me..

tflEOj

20 The Toung Surveyor's Gtride,

THEOREMlll ^

Fig. 38. If two Triangles have «3ch fide in.
one equal to itg. correQionding £de in the o-
ther (that is, « = e/f cb=fi, and ab = ei)-
they will alfo have = Angles opposite to.
thofe = fides (that a e = f, a=e,mdb=i).

Let the lioe ab be put upon the line ei. Then-
the point c will either fall in f, or it will
not. If it falls in f, the whole Triangles a^
gree, and therefore all (he Angles are equal
By the feventh Maxim.

Fig-^^.lic falls out of f, draw the line fc :
Becaufe by Hypothecs the fldestf, and ac
are equal, the Angle efc muft he equal to the
Angle ecf; hy the fecond S'ropo&ion theie-^
fore Angle! fe will be greater than Angle ecC
and Angle ifc wil be much greater than An-
gle icf.

Again, by fuppofition , becaufe^ f =:.
be, < ifc, willbe = to < i e f. Tlierefore-
i fc is both much greater thaOj and equal ta .
cf, which is impoiUble , and tberetoie c
cannot fall out of f. '

Tff£OR£i!if iV.

J^^.40.0ne right line CDfalling on another

AB, makes the Contiguous Angles = to two

right Angles. Let the line CD bejperpendi-

culat to AB, theD the Angles ADC and CDB

wijl

The Toung Surveyor's GaiJe* a I
will be right pr.jDiif! But if the line fall
obliqueljf as tD, raife theperp!ndicu]ar GD,
rf!%), becaufc the urieijualAngles ADE and
IsbB occupy the famepl^ce which the two
right ones ADC andCDBdid, therefore they
pgree to two right Angles, and confeguenily
to them (by 7 M.) Q. £D.

,--■'■ THEOREM V.

Fig.^i- If two right lines {BC^mi FL) cut
one the other in any point (A) the oppniite
Angles at the Vertex (A) will be equal ; that
18, the Angle LAB is = to CAF. Becanfe
BA,,flands upon the right line LF, LAB,
and FAB will he equal to two right {by the
fourth Tlmrevi.) Aid becaure FA rtafids up-
on BC, the Angles' FAC, and FAB, willbe
equal to.two right (hyt'^efame) therefore (he
Iwn Angles LiB, and FAB Taken together
wiil he unal to the two Angles CAF, and
FAB, i»?en together. But the common
Angle FAB-being taken away, there remains
the Angle LAB= CAF (by the third JUax.)
Q,E.D.

T.HEQREMi.VI.

Fig 4.2. If arighi line GO cut the two pa-
rallel rifthr lines (JB cFjfitfi the alternate
<(RLO, ^L. W BJ:0,C0I.) are equals.
SewiUfy, The exteroal Angle (GLB) isequaL

22 ThfiToung Surveyor's GwHe*
to the ipternal one (2.0FJ as alfo(< G£,S^
<LOC.) Tbirdfy, The two internal Angles
towards the fame parts together ALO COL—
to two right Angles : Alfo the <s BLO, fOL
together = to two right Angles.

DmoH. oF the firft part Draw LQ. and RO
perpendicalai toCP (rom the points L andO
and they will be alfo pecpeadicolat to AB(by
the 1 2tb Mjx'm,) now in the AS ROL, LOQ,
the fide OL, is common to both; R O =LQ.
(A> tie m Def.Jind .•.<LOR=<LOQ (hy tba
frft Prop.) alfo <R0 L « < Q.LOV. <
BLO =:<COL (bjtbefeemiM^x.) which
is the. Firft Part.

Second I'arr. Angle LOQ. =<ROL {hj **»
Tirji Pjtt,) and < RLO= <GLB (bj the yti
Prop.) :./< LOQ.=< GLB (bi tbejrjl Mvt.)
afterthe fame manner may <IX)C be proved
= to < GLR which is the fecood Part.

Tbe zl Part. Angle GLB=<RLO
(^ tbe "jtfi Prop.) <COL was proved = <
RLG (in tbe 2l Part.) bot< RLG -\- < GLB
= two right <8 (*; tbe ^h Prop.) /. < COL
"|- < RLO = two right Aoglef , as aUb <
BLO-t-<FOLQ,E.D.

THEOREM VIL

In any Triangle a be, the three Aisles
taken trgether, are equal to two ri^t ones.

The Toung Surveyor*! Guide. 23

DEMONSTRATION.

/%4^. Let i be drawn parallel ro theBafe
ac, theo tbc < a will ;=: < dba (by the stb
B'op.) and < c, = < ebc (^ tbs SiIkPio^.)
but < d ba -\-.< abc + <: cbe = to two right
Angle* (hj tbi 4tbFittf.) .*. < a -}- < c -t- < ^
abc = two right Q, E. D.

CO & RO L A RT.l.

Hf Dce by Having one of the acote Angles
in any R'dangled a, you m^y find the c-'
thcr kv takirg ihe Angle out of 90 Df gr»s,
and that which remaios will be the Angle
required ; io thatooe Angle is the Comple<
Dient of the other to 90 Df greet : If your
Triangle be obnifeoracitfr, any two'of the
Angles beirg known, the ^d is known « by
taking (he Sumoi the two Angles known,
from 1 80 deg. and the remainder is the other
Angle.

CORROLJRT. II.

J^.jj.lfany fide ofaTriangle be produced,
the external Angle o will be equal to the
iwo Internal and oppofiie Angles b and e.
For the Angles b and e together with d, are
equal to two ri^ht ones (^ the Preced.) and
(b alfo are the AqglesO and it,(by tbet^tbJ
where

14 ^^ Toung Surve^orU Guide,
whenfore O miift be egaal to b added to
«, bccauTc tfigdther wiui d, it makei tura
right ones, as ihey do. Q. E.D.

CO R^OLJRT. III.

J^g. 45. The internal Anglet A, B,C,D,E,
of any Polygon ABCDE are equaUo twice
as m3ny right Angles as it tiai £dn, except
foui.For everyPoljg'ja maybe divided into
as maiiyTri3ng1es,excepttHro,as ithasiides,
by lines drawn from any Angle D to all the
T'cft, except the adjoining ones% and Ej but
each of tnofe Triangles contain three Angles
= two right ones {by the ytb) therefore all
the Arigles of any Polygon are equal to twice
as many right Angles, eieept four.

CORROLJRT. IV".

fjg.46- In any PolygonA B CD E, the iidei
being produced will make all the external

Argles a, b, c,d, e, equal to four right onea;
jpor each internal < Awiih its^eiternal •< a, is
equal to two right Aigles (by tbe^tb j)cOnre-
quently all the internal and external Angles
are equal to twice as many right Angles as
the Figure has Hdes. But ail its internal
Angles are equal to twiae as many right
Angles except 4 as it has fides ("iy ibe Ufi Cor.)
therefore all the external Angles taken- te-
gither, are equal to four right ones.

COR,'

The Voimg Surveyor's Cuiik, a S
CORROLARTV.

. From the third Corroldiy ive may de-
duce a Method lo examine whether the
Angles of a Fifld be raken light' or tvi^^viz.
Malliply the number o\ Sides thereof by 2j
fubflrad 4 from that product, which remain-
der mulriply'd by 90, will give the Sum
of all th^ Angles, which Sam mufl be e-
quil to the Sam of the Angles taken in ih«
Field if rightly obferv'd.

Fig.^S For Eiample: L^ABCDEbea
Field bou:i(led wi:h ^ iiHes, tha Sum of the
Angles whereof is 540* which is equal to
tiie Number of fidts (5) maltiply'd by 2» ■
and that Ptoduft leffen'd by 4, multiply'd
by 90, therefore it is very probable that
thofe Angles were rightly obferv'd.

TtiEOREM Vm.

f7^.47.The oppofiteSides and Angles (^any
Parallelogram are rqjal^ and it is divided
into two f'guil paitB by ( a Line diawii
f[om one < to Its oppofite one which is
called ) a Diagonal Liae. B.'Ciufe O B is
ptraPel to DC ( h Def. 14.) the < OBD
= <BDC (by Prop. 6) alfo bec^ufe DO
and BC are parallel < CBD = < ODG
( by the fame ) .-. the whole < OBC =s
< ODG after the fame m4Rnst < O may bi

^

a6 The Toang ttrw/or'T Gttiiif*
Iheurn to be rq lal to < C. But /ince we
hare fbewn that rhefe Triangln Q. and
K which have one fide X) 6 common, and
two Angles adjacent td D B in one, rqua]
*fi the rwo correfpontKng Angles in the o-
iher, fhfiefore thore Tnangle»and iD th*it
p4:t(,are iqualby theStholii'infortiePrqp. i.

SCHOLIUM. '

Fig. 48. For rheTrianglft AEF and GFD,
having the Alrernate Angles EAF and FDG,
and AEF and FGD, and AFand FD tqciil
they are equnl, (by the 1/, ) and fince the
Trapezium BfcFD, with the Triangle AEF,
that is to fay, ihc Triangle ADB, is half the
Parallelogram, (by tbi hft) the fame Trape-
aium BEFD, with the TritDgfe FGD, will
fce hjlt the fame-, therefore the liM £G di-
vides it iotQ into two <qjal parts.

THEOREM IX.

jF^?.4P.ParanelogMmi having thefimfBafi",
and Ix'ng between the fatne Puralleli, are
co'ial. For AB - EC &*«. (by the ith) a
BAF = a (E C G ^ the'jfi) from hoth 6*
which take away thecommoa a DEF, and
there will remain the Trapeaiom AEDB =
Trapezium DCFO, to each of whieh add
the a BHC and then the Pajailelogrsm
aBEC ^ iPitallelogmm JBC6 ptr 2i M-x. I

^i Ttnmg Survejfor's Gmde. 27

TBEOhBM X.

Fig. 50. 'f rianglea en the fame Bafe AB,
mad being between iW fame Parallels CF and
AB if 9 always pqnal.

The Triangle ABC, ii f q«al to the
Triangle ADB. Draw the line I>fi parallel
to JVC, and the line Bp parallel to AD, then
th«r« will be mada tiro Pai^llelograins, A
CDB i and aDFB, which being between ih«
fame piTblleit afvd 6n the fatne B»fe^ will 1m
rq'lal to ons anotber (by t6e hfi-^ tut the
Triangle ACB is the half of the Parallelo-
gram A B C C. and the Trimble DBA is the
half of a PiTBlfclogram ABDF, (Sj tbt 8th J
Therefore the Triangles rt CB andADB^
{ muft be vqral, by tiie-6th Max.

COkROt ARt.

Trianiles having ■ the fame or rgial
Bifes Xd PrfratklogMms. and between ihe
fame iftarallek, «re jaU half thofe Paralleliv
gram.

THE OR EM XL

, ^ i^.jT.TlvrComplem^nta of a Pirallel<i.
gnurfve rqaal. Ii( (he PikraDelogram ABDC
the Ct>nlpkni«ms\^£H and £Gbl jr»

C 2 DEMOA^-

,28 T^e Tcmg Surveyor*! Curde.
DEMO NSTATIO N.

If HG and FI fa-* drawn through

■nv, paint E of the Diigonal CB paralW
to Al. and CD, the Parallelogram ACCB is
divided info lour Parallel<\grams, two of
rwhich-are about the Diagona), and the other
two are their Coinplcirifnts, whitli are I hut
ihewn tebe(^i;il, o ABC = to A CDS
and the <is H B E and EFG are = to as

JBE and ECG (hfi) If frdm the Eqiul
^1 ABC and CDB voa CohRtjQ the F^ual
A3 HUE, EFCandIBE,CEG there wiU re-
main theParall'IogramAHEF — to the. Par

(jrallelogram EGID (by si Jxiom.)

THEOREM XU.

F;>.52.In eve»y rpaangte TriangleA B G,
the Square of the fide AC, which is oppo/ite
*o :ihe fight AngV, is tgual to the Squares
of the other two fides (J B, CB)

D^roon.D.-awIC,BF,andBE,ParalieltoAF.
I' then you add the coiiimon < B^C <o (he
right Angles lAB, FAG, and therefore e-
-qial, llie wholes I AC. !FAB, will be rqial,
but the <s I AC, FAB have the two fides
w*i><"h rontaim tho^Angles e<jiiat (iji>/ J ?)
to wit lA = BA and CA .== FA .-. < lAC
■^ A FA.R (by Prop, i) hu( A TAG = 4-
th.t;ga:e ILEA and A ABF=-t ParaUelq-
^aia

The Toung Siirveiilrr^s (TuiJe; 39;
gram AFZ the (b/ Piop.io) tturefore pquare
LIBA =the PatallelognmAFZE. Ir inighl
te Ihewn with the fame Eafe that th? Square
BXCH =lhe Putdlelogltim CZER. Q, t. D.

T HBO HEM Xllli

fig.^^.An<{SCA) at the Cetiter 11 double
to the < (JFB) at the G'truinFerence when
the fame Arc (AB) is B ife to both Anfiles*
Thii Prop, hath three Cifia, The fitft in
when the fide (CJ) coiticides with the fids'
(.AF). For then CF = CBi becaule both 3t»
drawa from the Center to the CirctiinFerenr^
c£ the Tattle Circle therefore in aCFB-lCBf
= <CFB (per fnp. j; fciit <BC*=<
CBF + < CFB (pcrSM. 7 fref.J .-. <;
ACB is douUe the <CPB which may the (irft
Li the fecood Cife CA and CB tall with-
out AF attd BF. Then < X C A i«
dotible < A FX, atid < XCBiidoobij th»
<XFB (ijtbefJI-CiJi} Tlierelore the wltiiU
< ACB is donble the whole < AEB. In ihe
third Cafe RK cuts C A, and the < AKB :'s
wholly without the < ACB Draw K C L
Ihtn < ACL is double < AKL (by tbe frl
Ctfi) and if < LCB and its double < LK B-
be taken away there reintins < A B doab.e
■6 A KB. Q.E.D.

C 3 THEO--

9 o The Toung Survejor't Gurje*
THEOREM. XIY.

All fimiW Triasf^lei have their fid^s a-
bout their fqual Argles nroportiora). For
if they were inlcribtd in Ciccks, (heir Sides
would be C hofdi of fimilar Atct.

THEOREM. XV.

F^. T4. If in any Triangle a tine be
drawn parallel to the. Bafe, that Line
will cut ihe Leg« proportiona!?. In the
Triangle ABC let the Line DE, be pj-
rallel to BC : I fey that i^D, is to AD 3s
AB to A^ and AB : BC :: AD: DE. Alfo
DE: BC:AD:AB:or AD: AB :; AE: AC.
For As Atif, and -DHare fitniUr becaHft

<D=-<!Band-«E= <Q (bj the6th)
^i(t < A is common to b«h .'. theif 6ides

about their tqjat Angla are ptoportional

Of Rijiif Litttt gf plied to a Circle.

DEFINITIONS,

I. Every C-rcle is fuppofed to be divid-
ed into 5^0 D g. and each Dig- iott) ^0
parts, called Minutes, and each Minute into'
Poparts, called Seconds, ifc. -^ny Potti-'
on of the Circumference whereof is an Arch,
and

The Ttmng Sitrveyor'i Oiade. 3 1
and is Meafured by the. Number of Degteet
it contains.

2. >■'/.??. A Chord is a Rigl^t Line
joining the Extremiiiei of an Arch, as
AC, is the chord of the Arches ABC, AD::.

3 A Tangent of an Arch w a Ri^th'T
line drawn Perpendicular to the end of the
Radius or Semi Dameter, pafllng through
one end of the Arch, and i(s length is li-,
mited by a Higiit-line drawn for the Cen-
ter through ihe.oiher.End of the Arch, which
is called the Secant i thus BM is the Tan-
gent, and FM the Secaot of the Arches
Afiaod AD.

'4. A Right Siae ia « Righr-lint
draw* from one End of an Arch, Perpen--
dicalar to that Diaimter pa0ing thtoogh'
the other End , w is half the ( h^rd of tn«
double Arch; AE it the Right Sine of th»
Arches AB, and AD- And here 'tis evic'eor, ■
that the Sine of 90 D.'g. which is fquilta "
the Radius, or Semi-diimeter of that i, ircV, -
is thegreatefl of all Sines, the Sine of au
Arch greater then a Quadrant, being lefa-
than the Radius.

5. A Verfed Sine is the Segment of
the Diameter intercepted between the
Arch, and the Right Siw, EBlis the Verfed
Stne of the Arch AB, and (D of the Arih
AD.

6. The difftrerc*! of an Arch from
' 9. Qaadrant,, whether it' be greater or left,

C 4., is

5 2 The Toung Surveyor's Guide:
is -call'd ifs Compleimnt, GA is the Conv
t)lemer.t of the Archfs AB, ADj HA is the
Sine o\ the Complement, or Gjfine, GI the.
Tangent of that Complement or O-Tao-
gent, F 1 the S.cant of that Complement,
or Cc-recant.

Tlane Trigonometry^

Is tbe.Menfiiration of tTi« S (i<s and Ar-
gles of plain Triangles. A pUin Triangla
has Jil paits, viz. -Three Sides and three
Angles, whereof any three being given, ex-
cept the three. Angles, the other may be ^
found by Trigonometiical Calculation.

In ri^ht Angled Triangles , there are
feven Cafes, all performed by the follow-
jng Jxionu.

J XIO M I.

In any Right Angle Triangle, if either
of the Legs be fuppofed to be the Ridius
' of a Gird!-, the oiher L-g will be the Tan-
gent of the oppofite An^e or of the Aigle
at the Center, and (he Hypoibenufe will be
the Secant of that Angle : But if yon iin
agine the HypothenuH; to be the Radius of
a Circle, then each Leg will be the Sine of
its oppofire Angle, or of the Angle at the
Center, as is' plain fiom. Fi^. 5^.57: 5S;y9.
Iq

The Toung Surveyor's Guide. 33 ^

In the firft of which : B: {the Bjfe) being
made (he Radios, P (the Pirpcndiculur) is
ihe Tangent of thrAogle nt a,'the Cenrw of
(he Cirde, which is oppnfite toP, and the
H/pothenufe is the S cant of the fame Angle.

In the fccond of which, where P is-oiiide
the Radius, R js the Targent of the oppo-
fite Angle at the Center : O.

In the third of which wher« H theHy-
pothenufe is made rhe Radius, . P is ihfr
Right Sine of the oppofite An^le it the
Center. C

In the fourth of which H being a^o triads
Rarfioi, but c the Center of (he Circle, B
will be Sine of its oppofite. Angle.

CASE. I.

J^ 60. HyportienuPe and Aogles giv<n,-
either ot the Legs required.

^ be =14457
la i-a b c, given< S t(qba,and

Praportitm.

Ci > <:ba

<cs!l CC3^

\s7 V 168 i 61 -

S'90':446;:< >22'.3o' -?

_ 407-
C 5 O^it*-^

/ } 7be Toung Swvejor*s Gmdt,

Operatun.

To _ the Lcgar of h c 446, 2. ^44044

ftdd the Sioe ct Aoglc c 22*.. 30' 9. (82S40

12. 226884.
Sum abate, Rad= Log. t>a 168^61.

By GttBtert Scale.
The extent from the Sloe 90' , to
the Sine of the AcgU c 32- 30 od the
Line of the Sine*, will rfach from b c 44^.
•o ba 168. &i on the Line of Kjoiberi.

CASE 11.

Que Lfg and an Argle glrcni the
other L'gitquired,

Exampk.

In the & al;c,giv<»^ >rr^'d ca,

^^(Lc,= 22,JO>
PfoportioM.
Rad: ba : : c f, ic: ca, le. T, 45,; 168,
61 :: T, 67,30 '407,^.
To the Ixgir. ba 168, 6j 2» 2368S4

add thee t, c 22^30 10, 382776

Suoi abate,Rad=Lrg, ca407,6 12.6056*0.

CASE ill

One Leg and an. Angle givejt, Hyi»lhe-.
nufe required.

ExampU.
In tliej^ab c, given ^ . % if q'lii'd he

(Tic— 22',30'>

. S,ic:ba::ttad, : b f .

Operation.
Tfl /r,co. S, <c 22°., 30*. o, 4171^0
Add Lrg^ir, 6a ij58, 61 2, 226S8t

S^m = Il^e!.:f><: 44^ 2< '^44044

. - ^ Qvnters Scak. ■

-The E«en», from S, i c 22' 30'. To the
S, 96' y on the Liils of Siges. will reach
fronibaid^, £1. to be 446 on the Line
ef Nfimbws.

c^.yfi rv:

One I/^ «ad ^ Hypothenufe given, -
the Angles ftquktd;

Iatbe^«bC>446^ >req«iredi5 .

^JfiSj^J Cb

' FrepanioK.
Alfcc:Rad,:: ba:S,ic
446:8,90'': i.i<8. 6i:S22', -30'

s[6 Tee Towtg Surveyor j fjuide* -

Operation.
To Ar,co,Lrgar,bc44* 7. 3?595<S
, Add Logar, bv. 68, 61. 2. 22688^.

SumS. Ac 22*, 30' ■ p. 582840

From. 90°, 00

Subftrad 22 30. .

/

• Remainder. 6 y'ao* = < 1%,

By Gmtert Scale,
The Exrrnt from 446, to i6r, 61 00 the
.Xineof Kumberi, reaches from S. 90*,
o the Sine 22', jconthe Liae ot SHnef .

CASE V.

One Lrg and the HypothenQfe 'givcD,
4he other n quired

'dca

- Sjbc==446 ?
sbc.givcBC Wtqoirt

^b^=i68,6i^-
ProportioB,
■^Vbe Angles being lound by the foarth

As Rad, : c t, < c : { ba : ca;

T,45:T 67s 30' ; : i6%\ 61 " : 407. 6.
Ofertttim.
Tothectj <C22*', 30' lo, 3&277fi
add the Log. ba i£8, 6r. i. 226084.

Sim,lefsRad,=:Log,ca407,6 12. ^09660.

7be Toung Surveyor's Guide, 37
By Gunteit Ssatr.
The extent from T, 45', 00' Ion iheLme of
. To the T,67',30' JTarg-nts

Reachetfrom 1^8 -61 > on the Line of
To 407- -6 J Numbew.

C JSE \I.

The L^s given, and the Angles re-
quired.

Prifportfou.

c a : b a : : Radius -. Tang, L c,

407.5: 168. 61 ;:T,4;° : T, 22°^o»

Operatic!,

To the Ar, co L?gar. ca 407, 6 7. 390341

add the L'lgar, ba, i68» 61 2. 226884

Sum = T, <c, 22—30' $.61722;.

- By Gimttrs Scale.

The.Eltem from 407, 6. to 18A. 6i on
the Line of Numbers , reaches from T, 4;'
00' to the T, ■ 22°. ^c'on the Line of
Tangents.

CASE VII.
The L'g8 given , the Hypotbehufa r«-

38 The Timg Sttntfor's Guijt,

{ac, 40^. 5-1
S req. b c-

The Angles being found by the 6th Cafe.
S. ib:Rad, ;:ac:bc.
S, 67'. 30' : S. 90' : : 407, 6 ; 44^,

To ihe Ar.co, S t b 67" . 30' o. 034385
Bdd -Logar. ac, 407. 6 2. ^09659

Sum = Logar. b c 446. 2 . 54404^.

By . Qmtm ScaU.

The Eitent from S, 67° 3c' j^ «n ihe Line of

To tfie Sine 90,00 f ^Simi.

Reaches- ffoin 487: 6 7. on the Line

• To 44$. o 5 of Nuiribere.

Of Oblique-Angled Platte Triangles.

Wherein there ^re 6 Cafei , and all re-
folded by the three followiitg Axioms.

J TIO M il

In all Plane Xnangles, the fidei are pio-
porrional to the Stfles of their oppofite
Angla.,

AJTIOM.

The Toutig Survrfor't QuUe, ' 3^

A X 10 M III

In all Flaw Xrianglw, -

As the Sum of the Legs of any Angle,'
ii to thfir Difference i

So is the T^Pgent of baU the Sum of
their o[^o<ue 'Miglet,

To the Taogeiit of hall their Diflfereace.

A XIO M lY.

As the Fafe, or longefl 5ide,
is (o iheSmaof the ot&t Sidesj ■ '

• So i^ the Diffewnce of thofe &4aJ, ,
To the Difference ol tb^ Segoients of the
Bafe.

€ A S-£' 'f.

Fig. 6f. Two Sides, and an Angle
oppQ&e: to one of thejn ^iv^n i the A^Dgle
oppofite to the other; rfqijijed.
EKimpk.

In the A h c a. 5c*£i? , \ " qair'd the

PrepBrtim^
c.h : 6, i d : : cd ! S/ 6 per-Al, 2. .
64:8, 22% gc:: iS5»< S, 56^15/

40 T£ff Toung Sarvejror's Guide,
Optratioir.
To the Ar. co, Logar.cb 6^ 9. ip^Sso
addihe ^ L-tg.cd.ii39 2. 14^142

"*^"'* Is, id 22-. 30/ 9.582840

Sum— Radiuf,=S. ib, 56' ij/ y.^i^fioz.
fji Gmtirt Scale*
TIm extent from ^4 ? on the Line of Num-
> j bur>.

To

teachei

ToS.

22° 30' > on
5<-i; j" Sin«.

CASE n.

Two S'dM and in Angle opt»nre to one
of them giveD , ihe third S de rfqnired.
Example.

cd=2i39 ^
Id the a bed, g Ten cb=:^4 Xrcqnir'db.
id22%3o'^
Preparation,
Bj Cafe the fitft find the Angle b, and
kaowing the Argle d, you wili find the
Angle c to be ici' I5».

Fro^ortioH. per Jx, 2.

S, i b : cd : : S, i c : b d.

S, $6. T$ : 139 - : S, loi : i6/[.

Of-tation.

A^caS, Lb 56' ij' 0.0807^4

a. 143142

y.99 i5"y4-

Sjbi— IUdiu8=L"g- bd, 154, i2,2i4S7o.

r, Google

■"■■''41:i:''.-oV.'r,

^Tbe Toung Surveyors Guide* 41 '
By Gto ten Sculf^
The extent from the Sine of 56° ij» to
101' J5' on the Line oF Sines » reachei from
139 to 1^4 OB the L^nei of Numbers^ -

Note^ That the Sine of loi' i;», is tba
Sine^ of the Complemeot to 180. d<grees
= Sioe of 71" 45'.

■CASE m.

_ Two A'-gles and a Side g'ven \ the other
Sideieqdiied,

ExaiKpJe.

given, ^id =22.30' reqa..^

FrapoTthn. perJxi.
S,i d :cb:;SZ.c.-bd.
S.22°.3o':64:: S, iCi 15: 16^.
Operatiati.
To Ar. CO, Sid 22° 30/ 0,4171^0

addthen^^'t'*'*'' S'-99i?74
I Lig,cb 64 ]. 8a(5i8o

Sum— Raditis=: Log, bd. 1^4, 12. 214914

By Gmteri Sculi,
The wteni from the S, 22' 33'totheSiBe
101° 1 5' on the L'ne of Sines, reaf hes from
64 to 164 on the Lfne of Numbtr".
Proportion.
S. i d : S, 6 b : : cb : cd

8,22.30:8,56.1; :;64:l30.

' ^2 The Toung Suroffj/or't CuiJe,

CASE IV.

Two Sid« and an Argle compKhendfd
bj them, given} the other Angle* required.

Example.

Prtftratim hj the third Jxim^
cd =1^9
cb =? ^4

Sam =cb^-cd =« 2oy;

Differ, cd—cb at 75.

Prom ISO* o"=rt«fcfrt^>ftiM«f« Triangle;,
aibmattioi, ij =to the given Angle.

R«iniin 78, 45 — [q rfie Sum of theoppofneABgles.-
,Remain;:^3pa2Jz::iohalf die Sum of the oppofiDe

FA FOR T 10 N.

cb-(-cd:cd i.cb::T, A^iiiT.i- X 4A

aoj : 7Si.'r, 3o"a2' J- -.T, irf'Ja'i

OPERATION.

ToAr. cwLog. ed-t-cbj&j ?. iSpajo^

Adding ^^''7? 7S _ , I 87S0<i

J-UbdJ

!S*r|- 9- 481737-

(a,;-3Hin ■) f,3?"

8>m.-Rad— T.iWff. J ( u':

cy«« V.

The Ttnm^ Surveyor's GuiJct aj.

CASEY,

■ Two Sides, Mi the Angla comprehended
g ven i the other Side n quired.

gi«n, . '2cd=i29 Vxeqabtf.

Prepiratm.
Find the Angles b d, by Cafe the fourth.
Proportion, per. Ak 2.
S,i b : rd : : S Ic : b d.

■. ^ "6 Operation is the iame with Cafe the
fecond.

C ASE.yl.

f^g.62. The thr« ffi^ea gjven-5 ihe Angle*
required,

^ , Examplfp

In theObl. A b cd Sy f^°57 ^q^j^ed th.

6'*""- ?cb'=5o ^■'^"S^"-

Preparation hy ^pra 4.

From the Vertical Anglf, upon the Bafe-b4

Let fall ihe Perpend icuUr-^ — ■— Ca.

Theadic^ E.IC J" U1CD2 i seg«nttjd,ab.
c d

44 Tibd Tomi^^ Survejor's GmJe^

c d = 70

c b = yo.

Sum = cd -f cb = 12a

DifK = c d — cb =ss 20.

Troportim per Ax. 4.
d b : cd ■+ cb : : cd — cb .■ df =s da-b»
105 : 120 : : 20 : 22,_ 8.
OptratiiM.
To Ar. ca Log. bd = 105- S. 97881 r

Y Log. cd-t-cb=i2Q I. 0791B1.

Add SLog. cd— d> = *o , o.,3oio3o

Sum— Ridiin=cLog. df 2^1 8. 10.559022. '

By Gmters Scal>..
The fH«nt from loj*).

To 1 2cC On the* Line o(

Will rfach from acr Kiimbett.,

To 2 2,8 J

b^=io5=Baff.
fd =22.8= Difter.S'gmentt,

Sum
D

In

'in 1 27-8 ; \ 7

> its T < 6 5 .9=d= < >Segmenf;

.'fr. S2.ijS /4i.7=ba=>S
Then the A^-gles are found by Cafe 4(6
of Right Angled Triangles^ ,
pyopvrtion.

fn the ^ c aJ> I j^^S. 90:: 41.7:5.76.30.,

The Toung SiirvPfOr'sGmde^ 45
T .1. ,1 cd-.Rad.:; ad : Sic

'■"■""^ " ^1 70 : S, 90: : 639 ;S,il5;-,«'.
^ From 90' oc*

Suh, %6 ?o.

Remainders 35, ;0 = i b
From 90° CO'
Subflraa ^5 06.

Remainder = 2 4, 54 = id.

To 56' 3C»
Add 65 06.

Sam =11 21. 36 = i c ina be d.

Pra&ical X^igonometry,

W^berthitbe Doffitne 0/ Fhne Triavgltare ap-
plied to Pra8ict.

IN thh Sedion, I Ihall trett 6n1y of Ttldi
Practical parts thereof, as The Dodrine
of Plane Right-lined Tnanglea becomes
fu'^tfi'ienr tc ; As

I. In ALTIMETRIAv Bv which
the Htight of any ObjeQ acMffible, or
inaccefliblp, may be found 4 Ai of Trees,
Steeples, Towers, fiT'c.

3. In

4$ Tht Tmng Surveyor's Gmde*

2. In LONGIMETR.IA : B/ which tTie
Diftaoce oi one Obi d from soy place, or
of many Objedi ooe from another, whether
approachable, or in-approacha^le may be
known, their Pofitimu Uid dowa, acd «
Map maJe of them.

Of Mimetria,

frob. X. Ofm Jhitttdetbatis Jaxfbk.

r^. 6i. Let AB be a ^ower , whefe
Weight you would know. Firfl^ At any
convenient diflance, ai at C, place year
Q.uadrant, or any other Inftrument you
make ufe of, and there obferve the Angle
■AC3, which let be 58% fo much is your
Angle of Altitude Meaiure next the di-
ftaoce between your Inftrumtot and
Toot of the Tower, viz. The Line
which let be 55 Yards j then have you
light Arigled Triangle, one Angle g given,
and one Lfg CB to End the other AB;
which you. may do as you wfre taught in
Caffi. of Trigonometry: For if you ta)(e
58rrooH>o, there rcmatn9'32 for the Angle
at A. Then fay,

Ai the Sine of (he ^ A 33 9.734110

iBcochc Log.otthc 1. 59740 "] Addrheiwotc*

Bate CO is >gerher andfrom

Soi]ttwSlae«fdie<i>G)S 9.929426jrhe Sum Sub*-

■ • I I'- flraft the firft.

To

..Coo<!k-

The Toung Surve;9r^s Ga/A. 47

To th« Log. Height of [he "l — — —
Tower, AB, 40 Yards. Ji. Soai jo.

■ ■ ■■!■■■ <

Ta (his 40 Yards,, yon innft add thtf
heighihof youiIrtAfuincntlromtheGraHnd,
In this way of takii'g Heches, the Ground
ought to be very Level^ or ynu may make
great midalcet ; Alto the Tower of Tree
mould ftand Perpendicular.

fVoi. 2. Of a« Abhude iimecefibls.

tn the foffgoing Figure , let A B
be the iTo^r or Steeple, and fuppofe
CB to be a ]™>te, or fome other hindranfce,.
that you cantipt come nearer thtn C\' plant
your Infirument, and take the AngleACB
' J 8 dig. Then £o backward any convenient
'"-diflancf, as to G, ihere alfo take the An-
gle aGB 38 deg., Thii done Sabftraa ?8
?fom 180, lo have you 122 deg. the A'gle
ACG, then l£2 and ^8 being taken from
180, remains 20 for the Angle G ^C, the
diflancs GC meafured is s.6. Kow by
Trigonometry fay,

_Al ihaStneof the i A 23 ?■ 5340?2

utheI.ng.ofthediflanceGC26 1. 414972
SoiB the Sine of the Angle G 38 9.789^2

1 '.204J14 „
to the Log. of the Liae AC 47 i. 6^0269
Agiin,

48 The Toung Surveysr'^s Xjuide.

Again, As Radius io.oooooa

Is to the Log. of the Line AC 47 i .672098
Ho is the Sine oi the Angle C 5S 9.928420

To the Log. Height of the 7 ii,6oo;i8
Tower <»o Yards. 3 -

Bit as I told you before, the Ground muft
he Level. However, if it be not, I will
ihcw yoB, ■ , '

Frob. 3. Hov to take the Right of a Tower,
Sec. when tbi Grmni either rifes orfaUi.

F'g.6^ AB is the Tower, CB the Hill
vhereon you are to take lhe< Height of
the Tower : Plant your Inftrumenr in any
plactof the Hill, a> atC, dirr^ (he Sights
to A, and fake the Angle A C d ^ which
let be 19 dg ^o Minutes. Take alfo the
Angle dCB; which 184?*, 50'i then mea*
fure the diftance CB 56 Yards, take I?*?*^
ihere remains 70° 30* for the Angle A,
then (ny.

As Sine 70' go* 9.97454!*

is to the diftanctf CB J6 Yards 1.74818^
So are Soih the Angles at C, 9.957276.

Mt.6o•■oc^ ■

1.7105464.

:iS.

To

To the Heii^loftheTjwer i. 73

^4 Yaids.

Tbv Toung SumejiGr^s Guide. 49
To take thia at (wo Stations, without
coming to the Foot of the Tower, is no
more then what has been faid before-, fot
you .take your An^lea at G, and then mea-
uire to E, and there in the like manner as
before, take your Angles again, thereby yoji
may find -all the Angles, and the Line /l£,
'then fay,

Ms the Sine of the Angle ABE
is to ttie Log. of (he Liue £A,
So is the Sine of the Angle AEB '
To the Log. of the H'right of the Tower;
AB.

P- oh. 4. Hov to take the Horizontal'Lms of c
. Kfl.

K^. 65. Suppofe KLMN an Hil),
whole Bafe you would know. Plant youc
Inflrument at K, and caufe a mark to be -
fet op at L, ^o high above ^e top of the
Hiil, as the Inftmment {lands fcom the
Ground- at K, and take the v\rg!e LKN
58 deg. Meafure the diflance KL itf Chains,
80 L in ks. Then fay,

As Radius 10.000000,

is to theLineKLi^ 'Chains SoLin. 3.225309
iSoift theSiHeComplementof K.;8^ 9.734210.

to p»t of the Bafe KN 8 Cha. 1 2.949'5i9
90 Lid. — •'

P Bat

50 TheTou^ urve^or^i Cwds*

But if you have orcafton tameafure rhe *

whole Hil), plant a^ain your loflnjnient

ar L, (or.M,) and take your Angle NLM,

which let be'46 d*g. Meafure alfo the di-

llance L M 21 Ciiaioi: l^en ky^

As Radius loocoooo

Is to tie Line XM 3i Chains 1 323219

So is the Sine of the Angle 9831:934

MLN4«°. ..

To thepart of the Befe KM 11.1791^3.

Which I V Chains 12. Lin. added to S
Chains 90 I/'n. makrs 24 Chains, 2 Lin.
<or the whok BafrKM.

I suntiomd tiiis way, fos to aake jcm
tinderlland how to rake part of a Hill ; for
many times your Survey may end on th«
Side of a HiQ.

' But if you fiod 70D avetotake ivtlu
whole HilU'yqu med not take Co mqcb paint
as the fofmer way. fe» thus : Take, » bt-
fore,|he Angle K j8 d«p. MeafureKL-Theo
at Ltake the AngU KLM 78 deg. Sofe-
tiraa thofe 1 from 1 80 deg. Reiii8tiK44
for the Angle at M, Theu fay,

Aa (lie Sine of the Angle M.

ittotheLog.Df the Side KL»
^" So, is the Sine of the. Angle at L

19 the Lcg.of the Safe KM.

The Towig Svrve^&r'a Guide* %t

fVo*. y. Wmtotaie the Althsde 6f an Gb-
. jfB ^.mding upon a H'lB^ htaccefible.

_ Pif. 66. Suppofe N O to be the Ob-
je&, and you ftrnding at P were requi-
red to find the hetghtti thrteof, '

Firfl» upin Paper draw a right Line at
pleafnre,- as Q.T , and make cfioice of Any ■
Point at plealure, as at P, for the place ol
ywir flanding ; then with a QoadniDr dirw-
trd ro the Top of the Ohjt&, von find the
l>gr«eB cut to be 40°. ^2', and tften dired ihk
Sighrs to the Bottom of the OtyjeQat Oj
and let the Degreees ciube Hf'.if, ■'■ !' '

Then oprn P, prottaa an i (tf 40 ° yi' and
draw the Line P w at pleafure'^ And an i.
uf 22'. 2;', anddtawtfie Lim P c at plea-
fure,

Secotidly^ Ro forwards in a right Line to^
wards the Obj-pft as at R, aia 5 feetj and
there dirfla your Sights to the top of the "-V
Obj'fdt at N, and jm. wil7 find fhe degreei
cat tobe6i*-£2',t}iroiKh|whi(A-drawa line ''-".
« pJeafine, at R S, croMing the line P w in
thepoimM, the top of the Ohj^.; Froa»
vAKXitt a Perpendicular let fyX\ open the
Gronnd-Un« P T, as KKj that line (hall
be «gi>al fo ^he AUiiadc and ot the Hi]],
aird the Objedl together , (cnti Jhea
the SSgbti to 0, and it-jv tbt Lhte R f,
■ixn'wg the tint Fc in theyoint 0.)

53 The Touiig Survey cr^s<juiJe,

Now by the Inffrfrdions of theft four
Liiirt. Pw, Rs,P(', Rf, there 18 conftiiuted
lour Tiiangles, w'- PNK, and RNK, boll
Itieht Angled at K, and PNR, and RNO
Obliq'ie apgled ; By the rtfolving oi which
from the difiaoce (Deafured PR , and the
ftvttal A':ig\ti nbCetvtdy arRandP, you
1)13/ find the required Altitudp.

I. In the OWiqueangJed Triangle PNR,
Ih^re ij given, the Angle NPR 46*52', and
ihe Angle NRP ii8*28'i for it ii the Con;-
plememof the AngleNRK 6i'*82'to i8o'.
And the Side mejifured PR, 212.5 FooN
And having (he Angles at R and P, the Sum
of theinis i;9°. 10', w'lich take from iSo,
there will remiia 20' $0' , for the Angle
PNR. From which Triangle given, the two
oiher Sides PN, aod NR may be fouod by
Aiioin 2. thus,

AsSineof ihei PNR 2o'So.
Is to the Side RP Log. 272 ;
S) is the Sine ot NPR 40* 12
To the Side NR 3^0

And fo is the Sine of the Complement of
6i\%2'=^ ilZ' 7i>'(ortheLmp,) To the
biJe PN, 71?. 66.

In the Right Angled. Triangle RNK
rtiere is given,C!) The Hypothenufa RK =
= 80 Foot f2) The Angle NRK«I^3=2d.
U'lwreby you may fiud NK, by j^afe t.of
itieht Angle lilain Triaogleii tJ»M\^

A

The ypung Surveyor's Guide. 5^
Aa Radius i Sine 90 i.
Is to the Hypoihenufe NRitSo. ^ '
Sa is rhe Sue of the Angle NRK 61. 32.

To the Sine of N,K 3^5.
Equal to the Height of the ObjeS and'
the Hill together.

And To is the Gofioeof NRK, via. RNK'
2S, 28 . To (he Logar fide RK, 179. 4
Foot.

To which, if you add the meafured d:-
ftance PR 212. their Sum will be 391.?,
for the whole length PK, Tht-n,

In the Triangle FOK, von have given,
PK*?9i.<)Foo^ andthe iOPK 22\ 2'!..
hy which you may find OK, by Ca'e 1/,
of T'igonometry BR, L, T. Thus,
As Radius, Tanp. 4.51/,
Is to the SdePK ^91. 9
Si is the Tangent 6t the LWK 22'. 2;'.'
To the Hf ight of the Hill OK 160. 1 9Foi)>.
Which fubtirafled from 355. the whole
Height, there remains 174.81 Fott tor tlw
Altitude of the ObjVa NO.

Of Longimetria*

Piob. I. Ho'v (/.'tiding npon mObjeS of
ahiowtt Hsigbt,) to find the diftmce ho:n
thence, to fome other remote Objed,

F^g.^ySippoCe CA to be the Jide of a-

Fort or fijlwirk 22. 5 Foot h'g^t and he-

ing upon the P|glform at C, yoiuf-e a

D 3 Tie.,

34 The Toung Surveyor*! Guide,.
T'ce, or other Objefi it B, vrhofe diftance
TOU would knour from the Foot of the
V41 at A.

Th:; LinM ABand ACbeing drawn, 3nd the
he'g'iihof the Wall 22. 5: Foot^fet from A.
to C, where by your Iiifirument directed to "
B, you find che Degrees cut to be fl'. 2 s'»
which AogW lay down; fo have you the
Righr-argled Triangle CAB, in which there
It given, (l.) CA, theheighthof the Wall
2-2. $ fact (2-) the Angle obferved at C»
.77'-; 2;' Di'g. by which you may find the
aittance AB (hy Caft 2. of Ri^bt JvgUi
plme Triat^Uf.') thus,

As Radius, Tangent 4; Deg.

To CA, the heighth of the Wall aa-, y
Foot.

So is the Tangent of ACS, tfe Angle oL-
ferved, 7I.25 Deg.
■ To-the diftance AB, 66. 28 Foot.

And if you would find the Length of the
Line CB, you may (byCaje 3 ofR^btA'gt*
TrimgU) thus.

As the Sine of the Angle obferved at C
71 ^ 2;' Deg/

Is to the diftance BA, 66. 2tf Fopr.

So is the Radibs, S'>ne siQ D'$-

To the Line CB, 69- 98 Foot.

Fig. £8. Is Supjsofed to be a piece

of 9 River, and you meafuring along

one fide of ir, would as well know the

Breadth of ifv w »Jfa mak« a true Plc^ there*

■ of.

The Toung Surveyor' t Guide. %$
of, potting down what remarfcable things
are r«n on the other fide.

Being at ©I. the firft Station, caufe on«
oF 3'out Afliflants to go to the next ben4
of the River, as © 2- and there fet up a ■
mark for you j then fee what Angle fioin
the Meridian ® i- ® 2 makes, which l^t
be N. W. 6 drg. alfo feeing feveral marki
on the other fide of the River, take their bea'-
ings, as the Houfe A which ftands upon the
Bank, and is a Mark for the Breadth" of the
River bears N-W. 52 dtg'-ees, the Wind-mitl
B up in the Land, bears 1^ W. 40 d)g the
Tree C by the Watei-fide, bears K W 17
dfg. atl this note down in your Fi«la
Book, and meaftire the diftance irom ® i ro
® 2, 1^ Chains, 20 Links. After this conm g
to. s> 2, feahow the next bend of the River
bears from you, vhi. ® 3 ; which let be
N.E.l5f d«g. See al(b how (he Hnufe A
there bears trom you, viz. S. W. 20 de g.
,- the Wind-Mill S. W. 50 deg the Trte,
K. W. ■jj'- -A^^o ^ y°" ^^ gf'irig forward
- if you fee any thir g~ mere at tliii ftcond
Station , take tfce Bearirg thereof, ar a
Aoted Caftle D upon the Land, bears NTV.
23*, as a Church E clofe by the K'ver
BrinkN W,4'.meafurethe diftanci! from 02,
to »3. And p'aciDgyourInflrimentat«3, ht
Chmch bears irom you N W. 88 d g. 'h«
'Caftle up in the Land at D you cannot ''«!'
foi the Chutch, tlierefore let it alone tor
D 4, .the

$6 The Touag SurveyoT''s Guidi*
•lie nexi Station. Bur bete you may ft*
forward a liitle Village F, (he firfl Houfc
thereof bears fromyou NW32* deg.Meafm'e
ihctiiftance from© gtoe 4,andPlaiitirgyour
Inflrument in ®4,the fitft Houfe of the Vil-
lage F bears from you Smth-Weft 32(?.and
iheCaflle D, which you could uof fee at
the third S'ation, S W. 24* Havirg pit
down a)] this in your Field-Bock, it will
be as follows,

-^.N.W, 6^ 18 Chains 21 Links ,,
% )ATr« upin the Bank of the », ^ ,(

S^ River bcirs.
%ik Wiad-Mill upo
^= ( A Houfc on the B

{

® 2 N. E, 1!'. i8Ch8ins2p Linkf.

The Tree N. W. 77° 00 ■) ^hf fc look 10 Ob
The Hoofe S. W. so 0= t '^ '^ ^ "r. .

CAOnisfjrnp intheLandN.W. 38. 00-) For-
2 AChorch upoo the River N.W. 4 ooS-wardOh
C. Bank ifervitio

'Aj-^j N.W. ij'.ao Ch. (oLin.T
■4mc Church Bean N.W. 89 "rThefc look kiok-
}oThe Caflle cannot be Ceen > ward to Obf. ® 2.

0?N W^ si.""' ''"'' ^""*' S " ^""''^ '*'*'"•

0;4. .—

( The end of the liri'e Village S W 51%"^ Thefe ref-
«■ The Caflle refpeftitrg ® 3 SW.a. >peflO 3 ,

I, in the Land. S. 24,^ and e 2.

The Tmmg Surveyor's GuiJe. 57-
To rntraa tMs, draw the Line N. S toe
a Meridian, and laying your Protjaiftor
upon it, the Cencer thereof to © i i againft
N.W. 6' make a Mark for ihe Line that
goes to a 2. Alfo agiinft N. W. 17* make
a Mark (or the Tree,iind againft ^o' and 52"
for the Wind-Mill, and Houfc , Tiien froih
© I, through thefe mafks draw ihe Linei
e A, oB, ©C, 02. Secondly, Trfke troflj
your Scale iSCoainsand 20 Lin. and fcC
it off upon the Line ©2, which will reach
to ©2. , There lay again the Center of
your Prorra<aor j .the Diameter thereof Pa-
rallel to the Liiie NS , and make marks as
ydu fee i;it>ie Field- BiDk,wgiJnflN E !;*•
N W 77* SW 20*, aw so\ KW28',Ny
4% and through thefe ma^ki draw Lines,
the firft Line . direfls to yourthijd Station ;
thefecond Line NW 77' direa>.you to the
Tree Cupon the River Bank, for that Line
cutting the Line i C, (hews you by ihe
Interfedion where the Tree flood, and alfo
the Breadth of the River^ Alfo the Line
S W 20° cuts the Line from the fiift Sta-
tion NW ?2', in the place where Houfe A
flood upon the Bank of the River. If theti-
fdre you. draw a Line from A to C it will
reprefent'the farther Eink of the River.
And fo you may proceed on Plottihg, at-
cording tn the Notes in your Field-tiook^
and youwill nor only have a true Plot of
the Rjver, but alfo know-how far the Wind-
; D 5 Mill

58 7h* Totmg Survtyw^s Gmde,
Mill B, and (he Ciftle D Hand from the

Water-fide. For if you take the difbnce
b-Twilt any (woof the places, with your"
Compaifes, and try it upon the fame Scale
th« you laid down your Sationary di-
flances, gives you the diftance required;

fi'o^. 2> To fni tht diflmca betmeeH awj
two Placet^ b(ab removed from the Obfenttr.

^g- 69- L?t the two placet Iw B and D».
ftnd let their diflancei bie required by aa
Obferver llandirg,at C,

I. Let the Angle BCG b* taken, be-
twefn oqe of the Fisceij as B| and any vi-
fible mark ^ fuppofe G flanding about tha
the middle Qf the diftance, and likewife ki^
the Angle GCD fee taken.

a. Then leaving a vifible mark at C^
-Jet the Obferver go backwards into another
Station asatH, in fijch manner, as that he-
being at H might fee the mark C and G^
to a right Line ; and let hini meafurc the
diflance bctireen the two Stations C9tidH.

3- At H let him take. the Angle ^HG,
and GHP, as he did before at C; Thia be-
ing, done in the Tfisngle HBC, becaufe the-
outward Angle BCG 'is equal to both the
ibward and oppofite Angles BUG and HBC,
therefore by S ibflraaingBHCout of BCO,
there wi31 remain the Ang'e HBC. ThlM
all the Angles io the Xriaogle HBC, and

The TbitHg Satvsyor^s Guide. 59
iheit^HC iMing given either of ^eothtr
ttvO'Ades are found by the third Cafe ht
Plwe Triangles-.

. Agiin,' in the Triangle KDC, ehe Angle
HDC, and either of the fides CD or HD
may t>e found in the fame mannen

Lofily^ In the Triangle BCD, the two
Sides fiC and DC being found (as is 'alrea-
dy tatisbt) ani the Argle BCD, by Obfei-
vsh'on , ..thti other two Angtes CBD and

'£Dfi, may be found hy the fourth Cafe
of Plafie Triangles, and cnnfeq'fcntly the

• Side BD by the third Cai'e of PlaniTriangles,
MFhicb is the dillance required.

0f Leveffin^y or Meafuring the Ine-
' ^aSitjf iff flaces^ as to their Heights*

Fig.'-r^O find out the difference of heighrs
. 70-, X of oiKplace from another, in.the-
rificg and faUiag^ which is of conftant ufe
in cwve/ing, ot Water, either above the
GroHad tor i^ountalns, fJfc. or under the
Grotvd for Adyts or Soughs, (^c. Let
Jiout Inflrument be carefully made, »jirhe-
ithexitbe a Qjisdrant, Water-level, or ang-.'
ether ', thR befl I Account to be a bra& T.
fitt fights upon the top of the T, to be Per-^
fpe^ive Glafles, which mull be tried before
ttfcd^ and tbe Gla^lfs are to Hand alw^s
«iK w&j^ tluwill eodine longer SiatioBs.
thao'

The Toting Surveyor's GuiJe.

1 ordinary, and is for many reafoni the

I, it fubliantially made, and there muft

two maik Boards placed upon quarter

M, that yocr Afllftants may lift them

her or lower, as ihey (hall be direded.

Then fet the Level at near at you can be-

xt the 2 Marks which your Afliflants

1 upright in ^eir Hand*, with the flip-

; Marks ; turning to one, caufe him to

d or fet the Hit and Black firoke enn

1 the Level fights, and fo the othirV.

difference of thefe fights, in Inches and

1 parts gives the Afcent or Defcenti

his is^ ope fimple Station ; but if it

res boihAfcenti andDefcents, then in a

fct down yoor Bark Stations in ope

nn and you fore Stations in another,

ip boih the Columns, and take th'c"dif-

e of ihemi if they be equal, the two

art Level,if your foreStationeiceed,the

nee IS lower, if olherwife, higher. Atl

lie will clear all. I am to give the

ice of heights of the places A and B,

ie Line of the Level -SB, chufirtg my

)tion at C, where I plant my Inftru-

betwir, the Quater Pikes A a"<*_JP,

ing my Level firm, (he Affiftah's

ip and down the mark Boards till

ys the fights take the Black (IrokfS

id E i in a little Table rnade, fit

e heights of ihofe flroakes from the

in two Coluninis, one for the left

HatJd,

"The Toung Surveyor's Guide. 6i
Hand, the other for the Right, as you fee in
the Table adjoining, \wbereiri AD (for the
lefthmi) J8 found (6 be four Feet three
Inches 4t of an Inch, aad EF (jor the right
Hjnd) feven Feet, 1.5.

Again, Let the Second Station be at G,
and the left Hand height FH be ten Feet,
(hiee Inches and a half, and the Righl-hand
height I K three Feet, 3.7 Inches. Again,
The third Sation let beat M,and the Height
IL 2 feef, 9,4 Inches, and ON 12 feet, 1. 5.
Inches. Lafily^h-t the fourth Station beat P,
and the height OQ three Feet i o. 9 Inches,
and BR 1 1 Feet 9, SInches. The Sum of the
heights on the Letth^ttis 212 Feet and
three loches, that of ihofe bn the Right 34
Feet' aiid 4,-5',Iiichesi thriif difertfice is
1 3 Feet and i', S Incbvt and fo much is B
Jower then A.

Stacions-

(fcightionthc
Left-hand.

Fecc- tn.

Heights oD the
Right hand.

Feet. Idchci.

I

3
4

4- 3. a
10 . J.J
3 94
3 10.9

7 ' tS

,1 11

11 PS

, 1 21 3.0

u 4.5

Sumot thcHights on the Bight hand
Sara of the Heights on ihc lett-bind

Their Differ.
And lb much is Blower then A.

6i The Ttung Surveyor's Guide,

I The TJfe of the Line of Prdportion^ or
HJumbers commonly cgUea Gunter's
Line*

TH E Irg-nious Mr Qmter anJfeverat
othen have fufficiently handled this
£ub}ed, thereforei might have Taved my felf
that tloi^lc% bat becaule it wilt be ezped
ed here, and the Book more aferul^ I (hall
lay fomthirg io that purpofe^ and begin
ficft with,

X^oratioK upon the Line.

Kaineftticn. by the Line ^yb^undefr
fiood from this one Tfaougt^r, is'z^ That
what DeoominaMpn foeve r the £ift at the
begituuQg of the Line is, that in the middle
will be ten tiiUfB, and that ac rTie end will
be an hnndred (iipeB- fo many : Which if un-
derdbod, it will [not b.e difiicutt to know
what the imiermediate Figntes aod ' partt
are.

1 Example t. ^

To find the place of 25. you may call'
the I at the beginning or the Line, hut 1
' t , th«n will that in the middle be 10, and
the twa which {lands, open the xi K.a-

n

The Toung Surveyor's Guide. €^
£i-it^ will be 20 j then count five of ih« -
grand DIrifions) where ftop, for Et hat ir
the place which reprefenta 1 ;. Where note,
that if you had efleem'd the i at the be*
ginning of the Line but I, that is, on«
vtenih, the place which now reprefenli 25,'
would fignify but 2- ; : Alfo ii you had
efteeni'd it as 10, then would the place .of
25, be 250; if iQOj then 3jQQ,if but cut
then but 025, ^c.

Example IL

To find upwi the Line the the place of
^6;^. Firl), e&^em th« i at the btg^nning
pf the Line to be. xoo , theniwill ihst ia
the middle baioozt^ndthf MUMitpwfiF^th^^
niiddle joqo. ; from which count fix of th«
6rand-divifioM ind a half towardt (4000)
and then you will come tp the pVace ot 3(5 50.
i^ow you mitft itoagine the 2 10 be % little
beyond that half (livifipm for in tbia and
the like examples," whffl^e wre are tp find ^P^^.^
places, that which \% Utjiiei n^A bf takei)
by eftinution. Sa have yoa the place
■ 7652. ■ '

Note^ 'By thefe Examples lad medtioned,
. yoq inay perceive that tlM ^igofeii I, %, 3,4,
F ?,'$, 7> 8, 9i do fomttiiaeifiigiif/' theiB-
\ felves aloM,. fonistijttMS la,. ;ao,'. jo,' fc,
^ i£Knetiin« iqq^ 300, goo, Q^c. 4.3 the
vork peiformi'd thereby Ihall require .-The

(>4 The Tmng Survejior's Guide,
firft F-'gare of every Number is always that
which IS here ftt down, and the reft ofthe
Figures are to be fujiplied accordiigas the
^aeftion (hall requirf. And by the varia-
tion and change of the power of thtfe Nain-
bets fromi, to lo, or loo, or io"o, any
proportion, may be wrot'g'it by this,

■ • General Rule.

Always extend the CompalTfS from the
UtR Kamber to the Tecond, und ihat di-
ftance, or extent, applied the fame vay up-
on the Line, (hall reach fron; ihe third to
the fqutth Number reqiiiFed.

Or other*iftj' extend ihe Compailes from
the fiFfl'NDlrtlW#W>'the' -third,' and that ex-
tent apjilied the' ^ittieway, fhall atfo reach
from the fecond to the fonrth. Either of
thefe ways will effeGt the fame thing , as
by Examples following 0iall be made ap-
■ e^t^^An'd it is neeeffary thus to vary the
roportion, fo as to avoid the opening of
the CompilTes two wide;

MttlcipVcatioK iy the Line,

This Rule whether it be performed ArJth-
meiicaily^ot' Ipftcumentally, depends ap-
on EurJids. El'm^ P'op. i. lib. 7. where it
is demonfirated, that if two Lines be pro-
posed

r, CoO^k"-' .

The Toung Surveyor J Guitiff^ S^

pos'd, whereof one is divided into diverfe
parts^ the Re^anglp contaiijed under thofe
(wo Lines is equal to the Reftangles con-
tained under the Line which is divided,
and the pans of the Line divided.

The propoftiDn it, .as one i& the Mut-
tiplyer:~-So is the MuUiplicand to the
Prochift.

Example I. ,

Let it be required to multipljr 8 b^ 7
-the PifopoHion is, a»r: is to 8 :: fo'is 7:
to $6. Therefore' eitend the Co'^paffes
ttom I to 8 i the fame extent will read)
from 7 to s^, which is the pr odud.

Example 11,

■ Let it be required to Multiply 37, by 5
The proportion is j As 1 ; to 5^; (6 is 37 '■
to iSj^

Set one Foot of the Compafrfs in I, and
eitend the other Toot to S ■■, that fame ex-
tent will re»ch from 37 to 18^, which is
the produft ' or 37, being Muhiplied by
5. Otherwife, fet one Foot in 1 and ex-
tend the other to 37 •, the fame extent will
reach f[oni 5 to u;

ExampU

6 6 The T9ung> SiiniejKr*s Omtte^

Example III.

. Let it be required W multiply 8. 75 by
3. 6. The Analogy or Proportion is, a*
I. to )^6:: So is 8. 75, to p.$. Set one
Foot in I, and ntend th> othtr to 3. £;
the fame extent applied forward upon the
Line will reach from 8.7; to 31. ^.

Diti'j&K by the Line.

. In Divi£on, th^ Qaetient contains Uni-
ty as often as the Dividend does the Divi-
(oi : It follows (hen from the <;th Dciini-
tioD to the %ih Book ot E«cliit Element^
that the Quotient is in Propeition to i,
as the Dividend is to the Dbifor. From
whence we may deduce the Proportion fol-
lowing, viz. As ^ Divitor is to Unity, fo
is the Dividend to the Quotieot.

Example 1.

Let it be required to divide 40 by S.
The proportion is, As 8 : to i::4o:5.
Set one Foot of the CompaiTes in 8^ and
extend the ocher Foot to i ; that fame ex-
lent will readi from 40 dowavardsto ;:,
which is the Quotient.-

Otherwife eitend the Compaffes from 8
1040 i the fame extent will reach from i,to^..

Example II.

'' Z-ttit be required to divide 356 by 12.
The Proportion is As 12 ; i ;: 3?6 : 28.
Extend Uie Gimpaflei from 12 to ^j6 j
the faitie atent will reach from I to 38 ^
which is the Qiiotent required.

YquI know how man^ Figares Ihould"
be in the Qnotient, by fetting the Divifot
ordetlj.itoder the Dividend, &c.

The- Ruli of three hy the Line.

The Rule of three by the Line mull la
performed by ths Jafi General Rule^

Example I.

If 3$ Acres of Land be worth ^4 Z. «
YiWt\ what IB ;5 Acres of the fame Lind
-worth by the Tear. Proportion as s6 : ^4: L

So 36: to 88. 6\p

Extend the G>mpa£les from 26 to i54, the
fame txtciu will reach from %$ to 88, 61
which is 88 i i 2 J. ^d. 2 q, lot the Anfwer
of (he Queflior,

To esOraS the Sipare Root by the Line,

Divide the fpace between Unity and
the given l^iimbtc into two equal parts l

* . Where

^

68 Th/t Taung Surveyor's Guides
Where ih^ DivifioD fallg, is the Square
Root fought.

Ev ample IT.

To find the Square Root of ^$. Ei-
tend the Compaiies from I to 3^, the
Middle way upon ihc Line between thefe
two Numbers is ^, which is the Square.
Root of ?6- In like manner yo<i mSj^Sd
the Square Root of any other Nimrt^B^

Of Meafuretn£, ,

A clearer Idea of which youcknnol have
than that giren by the Inge'nioi^ Mr Cnm, ia
his eictllent T/ealife of Fraaioiw complea-
ted, which is as' follow.

Every Magnitude i$ meafiij'd by fome
Magnitude ot the fliine: kind, a Line by a
lineal Foot, Yard, Cft- 3 Superficies by *
fquare Foot Yard, £5'c. a Solid by a
Cubicle Foot, -Yard, tfc.

The Lkeal Mgajiirc ishnamtoaU' .

The fuperficial Meafure may be concei-
ved, by imagining a Floor pav'd wirh
Tilea, each a Square Foot^; for then the
N unber of T.lts is equal to the Njmbfr of
fquare Feet in that Floorirg. Now if (\\s
Flooring be juft one Fpot broad, the Nuin-
-. ; , tier

The Tomg Surveyor's Guide* 6^
ter of Tilts (or of Square Feet) will be e-
qual to the Number of Lineal Feet in the
Length of the floor ^ hut if the Flooring
le 2, 3.-4>~ 5. tP'c, Feet bload, the Num-
ber of TileB, or of Square Feet, will be
twice thrice, four times, five tlmei, Vfc, Co
many Tiles Qrr Sqnctre Fea.) So ii the FJoor
were It Foot long", and 7 Foot broad, 7
tifliCB -M Tilei (or Square Feet) ^iv^a 'yj
theNumber of Tiles or Square Feet in that
Flooring.

The folid Meafure may be conceived by
imagining a Wall buiU with Srone«, each
a Cubick Foot j then the Number of Stones
will -be equal to th. Numbrf of Cubick
Feet in that WaH. Firft therefore,' if the
Wall be one Foot thick and one Feet high,
the Number of Stones (or Cubick Fset) will
be equal to the Number of Lineal F«t in
the length 0/ that Wall. Secondly, If the
WalJ ihoald be of the fame length and
heighth one Foot as bef re, but-the thickliefa
2, 3,4' 5, f^f- Feet (htftead of me Foot) ,
, then the-Number of Stones^/or Cvhkk Feet'^
will ccctdinglyhe twice,ihrice,fourtirnesfive-
limes Cc. and as many as before. Lafily^U the
length arid ihicknefs be the fame as in the
laft fuppofition, but the- heigKt (irflead of
one Foot) be- 2, 3,4, S Feet ; the Number
of Stones {or CMck Feet) will be accord-
ingly twice, Jttice, , four^times fire timej,
• Ce. what it Was in the foregoing. So if a
Wall

yo The Toung Swveyor's Guide*
Wall is feven Foot Jong, three Foot thick*
and one Foot high: From what hu fce«a
(aid, a Wall of fet'cn Foot long, one VoOt
thick and one Foot high confifts of feven
Cubicle Feet -, bat a Wall of feven foot ,
long, three Foot thick, and one Foot high,
cotiAAs of three rimfs &v?n* Cubirk Pert,
thatis, ziCubickFeet. Lafiiy^ A Wail of
feren Feet lone a<nd three Foot thick as be-
fore, but five Foot high, cciitains five rimei
as many, thar is five times s i Cubick Feet,
or 105 CubifkFeef.

'From all' which is evidenr, that in caflif^
up any Menfuration, iha Multiplier iq an/
of the Mslti^licaticuis is an Abflra3 number
. BSiyellasinalt orfaer Mullijilicdlions w^at•
foerer, which may prevent the talfe Gonfe»
quences ufually drawn from multiplying
Feet by Feet, »/«. That of multiplying by «
contra^ nu mber,as 3 /. 1 9*. oi-hj 3 1 ; 1 9 / : or
Half aCcown by half aCrowni which is con-
trary to the Nature of Maltiplicatfon, whofe
Operations are wily compendious addilions,
cither of the Maltiplicand or fome part of
it, <ontiDualIy toitsfelf or its part.,

Suppofe a Roof' in length 120 Foot on;

both Sides, And the depth of one Side 18

foot jthefe two numbers multiplied togethjfr

]^odcce 2i^ofoot,whicbis 21 S^uareff,and

- 60 .

Thif Tmng Surveyor's Guide, 71 ^
fioFoot/fhalis, lo Foot above half a
Sgoare more , it being maaftir'd by tbe
Squwe nf 10 Foot every way^ fo that 100 ^
Square Foot is one Square. ^

Brah, I. .To meafure a Qeometrical, ortrae
Sqttjrv.

Mulriply the length by the Breadth, and"
the prodo^ ii the Area (hereof.

Example 1,

Fi]g.7i.AdmiiKLMN,whore fidet is 5,which
Mulriplied by ?, being both the' Length
and Breadth, produce 9 for the Area^ ag
may be %n by the Sdume

Froi. 2-' To ^eafiife » Ing Squtre or Parah
lebgram.' /

Mhe

Muln'pljT (he length by the breadthj the;
product is the Area.

y Preb. 3. To meafim a Rhomhft.

Is is dcmonAiated (hj the gtb Theorem)
thatParallelograois having the fameBafe^and-
being between rlie fame Parail?ls are equal, _^
tAthat the Parallelogram A6DF is equal to thtugVl^
Kbombua a b fiF ; therefore if you intilri.

ply

The Toung Surveyar^s Guide.
\y BF one of the fidrs by OF or a k the
'erpendicuUr , the Produd will be the
Area thereof.

?:

Examol^l.

Let at BF be a Rhombus, whofe fideBP
js 40 Inches, and lei the neareQ dift^ince of
any two oppofite fidfs, which Uthe Perpen-
dicular, as ak = AB be 34 inches, Z de-
mand the Area.

Multiply BF =40
by DFxfH

Anfwer. 1360.
Trob. 4. To Meajare a Triargh.-

TheParallelogramBACEis double toA ADE
0)y Corrol-S*Jl)eoremr- lo). Therefore Mui-.
tiplv the Bife AE by half the Perpendiru-
U% DF, and the Produa is the Area of the -^
Triangle ADE.

Example I,

Let ADEbea Triangle whofe Bafe AE

= 2o, and the PerpendicuUr DF = fe,^

what it the Area. ^-^

Aafwer, 80.

ProK s*

VrtAlm ^. j

To' imafwB ia Triangle , tlie j
diree Sides ht\<o% given, wiliioat nndiDg tbe \
PerpendicuIaF. [

-R V t B.

Add tcgether all the three' Sides ;
ud from 4 their Sam fubfirad every fide,
which call the three DJfTeremes % Multiply
thefe three •differences, and the ^ Sum con-
tinually tpgether^ the Square Root of rhll
)aft produ^ ii the Area thereof.

' Having divided the .T-rapezium in-
to Triangles as the Figure following, add
the two Perpendiculars, viz, AB.and CO
. together, and roultiplj that Sum by 4- the
Bafe LK, and the fteaangle oi Prodti^
it the Area.

" ".'"^jBvinMpfe. , ■..-...

Tig. 74. Let.6iLDKbcaTrapn!iuin,le»'
tlie common Bafe KL be loo Inchei, the
PerpeBdicula?~AB 40, and CD = 14,1
demand the Af^ _

7+ The Toung Swrveyor't Cmde,

3700 Anfwer.
Rrob. 7. Te UStjfvrc my fi^sLir Fo^off.

F^. 7^ Multiplj. the Sum of all the Hdes
by 4. the ^ifiaoce of any fide from theCen-
terj and the product ii the Area, {or they
may be divided in as many Triangles as
they ibaV« fid^s^ aod tbofeaill .tquml to one
BDother.

■ Etmk^. ■

Let ABCDEF be a Hexagon , any 0}
whofe fides it 10 Inches, and the DeareR di-
fiance. from the Center to the middle of
an^fidfl i* $. 4'Iiich<ss whu's the Kxv^

Multiply the Sum of thtTidci =: 69
MlUlf^fcrfCBdiaiIir = 4. 7

383. o. Aim:

fi-oi. 7

The Tomg Suw^r's CuiJe^ 75

Every Circle ii equil to thai
. OUorg, or loi^ Square, whofe Length is
Mjjal to T the Circumference and Breadth
rtjaal to it< Semi Diameter. For a ( ircla
ja a r!4g^rPoI]'goa,h»'in^an infinite tiBoi-
. bejfof fid«4i.aiW Aerlefpre ihe Semi Kame-
ittt IS elyvays .f^ttpendiculir to ^oOe of> iti
fg^i. rWfee«*ifflfe. maltiplT- 4-' ^^ Circnm-
((Sence^by i» Semi^Diameter, and the Pio
jduS ia t« Ares; thereof ^ : .

'to !■ ^: ... V . - ? . .-; iiir'clf. ' " ' y-'-.' -'

Every Circumference ia more than
TripU ,tb*H, D»met5t4 bw the.meareil
i'ational Nopiber, ketwjfen the Diameter and
ihe Circumference is, as 7 to 22. Th«c-
foietf-Joii BfcuJ(ii5)tjt^^'tTi& D'anieterby as,
and divideth^ Pcodwn;<b|^ 7,-thQ'Q(iotieii«
viU..f^^ fciktte £irL-ii)rifn:ence.
idWatc'^EVery Circle ia equal to a Re^.
■dgle'Tsi^ngle, one a£. ivhofe Legs is the
Ra^UB, and the other Rigbt-liRe equal to
tnt Circonjference of rhe Circle.

'.StoewfigreiftiijrQiiinaUlliljt; the Diameter
ty, ^ part of the Circumference, the ^^ro-
^oA^Ulhe Aieai - '^'i " ■ ■ -

^I ., '-■ ■...'&» Othef.

■y6 The Toung Survey^J/GuiHe,

Otherwife Tqaare iheCianKtar, and mul-
tiply that t>y It, and divide that prodn^
by J 4. the Quotient it ibe Area.

^ob. 10. To fnd the htifth of mt Jrcb-Lim
of a CircU GeemttricaBy,

Fig. nS. Let A BCD be the Arch-Lint
gven, «h:ife Length \» rfguim).: Firjli^
£>iaw the Chwd • line J^, which ilwayc
divide into 4 equal parts, rtK» take one (^
. tho(e parti, and fet it fromO to C uponthe
Arch- Line : Thii done, draws Line ^ro^l
the pomt C, to the fitft iDivifioo, which let
be Ki this Jioe ai ^ the AtchLioe AB
CD, which doubled fltaU be the length «f
the Arch-line required.

Broin IT. To fni tbetaiffb df tn JfrfA-ffiw,
grMer than a Stmi-Cirele.

Til 77. F'lrfi, Divide Ae tatd Arch in-
tQ two <^ual,part9« a> DK } then divfdt
the Chord-Jim AD, into ibar eaual paitsi^
then-ai before draw the Line OP, which
Line being taken foortimet, u equal to ih*
Arch.lioe aDF. v. ' ^-

^ob' n.' To' Metfttrt tht Far^oinf » &t^

Fig. 78! Every Portion of -a Ciicle^
whicbcon'aiaed uniet'two Stmi-Dianieteri,

and _^

TlieTotmg Sttrv^or's Gmds, 77
apd one Arch-line is equal lo. ihat lorgT
Sqtare, whofe Ltngth snd Breadth is equal
to rhe S.'ini-Diaoieter, and i- of the Arch-

To find the Center of that Circle where-
of the Archline ABC is a pSirt of the Feri-
ferj.

■ ■ ^ RULE.

Multiply ;. the Chord Line, vis, A B'
by itfeI^ then divide that prodii£l hy the
.Verfed Sine BK^ then if you add the
Verfed Sine to the Quotient, the Sum will'
be the D'ameter of the Circle belonging to
the Segment. ACK j and half thereof wiD-
be the l^eini'£)iaineter AD.

Bcample.

Xet ABC be a Segment of a Circle to be
mwfared r ; Now it is not at the fitfl'inrlud-
ed with two Seml-Di a meters j you mnft
therefore find th« Caiter D, whereof the
Segment ABC, is a part of the Perifery
by the laft Problem} then draw the two.
Semi Diameters AD and CD; fo fhall you
include the Triangle ACD, inore than the
Segment ABC, Now firft meafare rhewhole
Figure ABCD by the^afl Problem j then
meafure the Triane'e ACD, and from the
Content of the whole &aor AECD, fuU
. E 5 ftraft

73 The Tcung Surveyor's Gvide,
flrafl \U Content of ihe TtiangU ACD. and
tilt Rpinaiinier is the Area of the Segment
ABC. ■ ° .

The Operatiou,

Take \ itfche Arrfi Line-. , The Perpendlcn. ED S-*

ABC 1* iheSerai diwieKr./L TJw Bi(c AC t$

8 ; of [fac Arch. (J - —

Sub.sd.^Areaorihf'riUii^. jf — ->
r 'Tike ;- 71. »

HTbe Atttof the a*.*
Triiade A CD.
. ■ ■'

You niay . jreafnre the Segnunt
ABC, by- multiplying BE by \ of AC»
and it uriU do well enough iat common

Praaice. '

froh. 1 3. To Meafvn an ESp^y Dt Ootk -_

R U ■ i' E.:'' \- .' ■ ■■' ,

Multiply the longeft Diameter, hy tfit
(horteft, that produft by, ii, andt^di--
vide the whole mpdaa by jf, whielj,i U-
the Area f eqtured. ■ ' ■

Froh. 14

Th* Tmtng Sunejor*s Guides i^

pro J. 14. To Meagre the Saperfitial content
of « Sphere &r Ghbe.

k U L E.

Mg: 79. Multiply the Diartieter ty ihe
Circumference, theprodufl is the Superficial
Content of the. Globe or Sphere.

Example.

Let A be a Globe , or Sphere, whole
fep(?rfioaVConffnr', or Area of the fur/ace
K reffliire^ r ! ftiuUipIy the Girctimferenca
(mhtcbkgiitted'hjPr^'UmS') ^^hyihb Dia-
meter 14, the prodndt it 6t6, the faperfi-^
citl Content of the Sphere reqjired.

Froh.JS'.'-'Ta Mea/ve the Superfciei of a

.{, ■ ;... Cow?.

' ' R ^ir L E

Multiply the flam heighth fey ^ the Cir-
cumference at the Bafe, the produfl is the
CcaHcrf^^Sutface i t* ivhich if y<)a add the
Area of (be iCifcle At tfle Sa^, you (halt
have the whole Superfidai Cflntent-

_E 4^ Pioh

, eft- The Tbtmg Swv^foi^i GiaJki^

Pr(£, i^. To Meafure ibt Stpnfduaf tjh
Fraftram of a Ccue-,

RULE

Add the grfarer and lefler UrcutnfereiiCB
oflheBafes together, ^ the Sum of whicfi
Multiplied by itftheiglith, producu tlu fu-
perfcial Cootent of the Fruflruin.

Fi. So. Let BCDE he the Fmflnim or
part of a Gone, the Superficial C«it«itihrre-
of is legtitred, the Ciraimference pf the
greater and If&rBafe being 6 and 3, which

added is 9, the 4. ii 4. ^, which 4.1! maltjpji-
«dbv i2,theheightbBD,ihefffodu<^ is $4 for
the tupeificislContent ot iheFrufiruniSCDE.
ittrfff, The Superficial Content ot a Cy-
lender, ii found by multiplying the Gilt .
by the heighth.

Jnather ^jy^

Firft ftod the length of the whok Gme
ADF, whereof AeFrufiramBCDEiia paitt
then having the whole heighth ot the CuDe,

mrafufe the. Superficies by the i-stft, /Voi.

then meafore the Supeifides of the top parr^

or IcCex Coite, by the 'fiinie Problem, and

fcb.

The TemgSarvritr's Gmtte, 8t
Subftraa the Cootent of tbe le0er Cone
tirom the Conteot o£ the greater ; and the
Remainder Qiatl be the Cootent of the Vi:^
QxJUA

r B.aS MB Jd XTO.

The Fruflrum Bf DE given ' tt>
Xnd AD tbe £d« o£ tile Cone Ulongins
to it. -

S OLE.

Multiply 1^ by BD, slid divide the ptA*.
dna by PE — BC.the Qjiotient is Al>
ibught.

Multiply DE = «
by BD = 12

which divide 72
by DE— BC = 3
lli> Quotient ia AD = ^

tSOB ZFlt XVIIL

To Sad theSapeificial-Cattent oE.de
Segountof^ Sphere.

82 The Tomtg Sunny^^t GuiJe,
RULE,

Multiply the Heighih by the Crfciiin*
ference of the Sphere, (0 which ptoiaQ add
the Area bfitt Ctrcu^lu B^/oMlhat Sato.
is the Area fought.

Prob. ip. 70 Meafurg dCuU.

^.''■*;^,

Cube the Side : That is, ipulfiply the fide-
of the Cube by it feff, and iftirptodbft a-
gain by the iide of the Cube^ Mrhidi Cube-
aumbex ia the S^lid Content thereof^

''' Tig. St.- Lrt ABqSJEFG reprefent a
Cube J whofe Side let be 30 Inches j Ide- ,
Hund the Content.

MlJtiply. one £d^. ^ ?o .
• byit laf -=' 5io,':

which produdt HwltspJy yoo ■ ■ • .'
again by 3* -^■-■

it prodnDe£' 2t<3oOi Co^t•■^

TBe T^uag- Surveys Gutde* 83,

By the Line of Ntmhers. ■

Extend the Ccmpsfles, .from i, to 30,,
the fame eitent will reach from 30 to poQ^
and from thence to 27000, the Content.

Pfob^ 20. To Miofure a 'SjralUl^ipedoni

^R Viz:

Multiply the Length by the Breadth ,
^ aqd, the produft by tfle £>epth ^ whieb
gives you the $alid Content.

Example.

Fig: 82.'Let ABCt)EFG, reprefent a
Pai^lelopipfdon 1 whofe length AB is 4a
Iflcbei^ the breadth BC .== ^o Inches, and
Depth CD = ly ; what's theConteot.

Length = 4a

Breadth = ^o •

l2Qa
Bepth ij

•op-

-J >8q0O;=

^ConKnf.

«<»,xr:

^4 TIj* Toang Survejior't Culde*

^oi, 2 r. To Meafve m QUbt ei SgCere^

To find tfie Solid Content, thcre.are €l~
■Vital vrzyt. At fTtft multiply the Cube of
the Diameter by ir, and divide the produft
by 21^, the Quotient ii the Solid Content..

2. Ot muhiply the Diameter, bj ^
part of the GioUs Superficies, the prodoa
IS the Solid Content : Or one' fizth part of
the Diameter muUiplyed by the S£herei Su-
perficies gives the ^ine^

3- Othetwayi, Multiply the Area of
the Circle, whofe Diameter is cqial to the
Globei Diameter, by -J; of the Diameter, the
produQ is the ?olid Content : Or, Multi-
ply the Diameter by -f ol the, Circlei Area,.
prodDces the fame^

Trvh 22. TofuitbeSoUdCtnte^efa-Cotte^

RULE.

By 9 h'oh. (btf going, find out the Are*
fjf its Bafe, and multiply that by ^ of ita
heighth, and that produdl is the Solid Qan--
tent ofit^e Cone rr^uired.

Example.

There is a Cone, the Citcomfereiw* of

whsfe l^le ii 22. i % and its heighth is tS..

1 demand

The Tomg ^mij/nr'sGuiJii 8j
t denaild the Solid content of fiich a Cone.
A? 32.

So is 22. 5 the Circomference of the Bafe.

To 7. 1 « the Diameter of the Baft.

Then Ihultiply i M. '. "hkh in 11. 25^
by i 7. lS2«rhich is 3- 58, and it produceth
40 281!, »hieh il the Superficial Content of
the Bali. Again, molriply If-. 286 by u
333, which is f of the Heighth of the
Cone, and it produceth 2i4.a4«i;7i the
Sniid Content. . , . . . „• '■

But here you are to obfcrve that the flanl-
ine fide of the Cone is not to be «ken foi
its true height, but a Perpendicular let fall
torn ite Veitn.to it. Bafe 18 ila true heighlh ,
and the fame ia to be obferv'd iB the. Py-
lamjd-

ftoJ.. 23. Te fill lis Mf Caileirt of »

Betureenthe Cone and Pyramid, this is
theDiffettnce. As the Cone hath « C^cnla
Bafe, the Pyramid hath a tight-lined Fl?ure
for ill Bafe,' fo that its Bafe and SopeificiM
are Ansuki , its Vetiei tenninatii« m a.
Soiot^

9S 7%t Totmg SurviyorU OuUe^

MULE.

Fkft, find the Sapeifkut Content of ihe-
fiafe : Thes nwltiply that by -f of (he
Heighth } ami it pcodHccth the Solid Couku
of me Pyramid.

IVofc 2\. Tt-Meafari tbt Frujinim of a Pf^
iamid or CoK?.

Fig. ftj. The Fnifirum here given to be-
neafared u ABCD, tht £de hi (he greater
Bafe A, being 34 laches, and the fide of (he
^eSkt Bife at B, 8 Inches, and (he length of
it I M so Fee* = BO: = CK 20 Foor.

IC is evident .that if i find the Solidity of
the whole Pyramid aED, and alfo the Sc-
lidity ot the leffer Fyramid BEC, and thed
Aib&aa the Content of BEC, from thp
Cohtfnt of A ED, there will irenuin
rhe Solidity of the Fruftrtim ABCD j and
certainly thii way of meoTuring the Fru-
ftnun oif fi Byranaid or Cone, is the moft
exa£t . ori any ^ and it may be eailly mea-
fbred: tht»: Firft of all find cut thc^eighrh^
of thewiiole I?yiainid£M^ which you oiaj-
^ do hy the following proportion, wis.

As the S:; mi-difference of the Bafes,
Is to the heighth of the Fruftrum,
■ ' So is 7 the greater Bafe,

"Xo the heighth of the whole Pyramids
UTiicte

- Which propwhon will hold good in
Cones as welt as Pjrainids.

Let AD be the Diameter of the great«f
Bar*, and BC the Diameter of the lefler
hak^ from B, and Q let fall the Perpendt-
cttUra BO and CK^ thentfliall OK be equal
10 Be, and theStifli 6f AO and KD are
(be difftrefic* ef dxe-Dzmet^naf the Bjfeft
AD and BC| and conO^iently AO th*
Semi difference, and BO the heignth of the
Frftrunij. and :^ is ~ the fid^ of the grea-
ttr Bjfe, and.EM la the heighth of the whole
Pyramid. Then,"' ■ /

AsAOtFie S?mi-diffiren«ef AerBiaimtet!^
Is to BO (he hdghth of ihe FrDflfoxn,'.
So is AM (4- thi greaP Dijmttir,
*%o EM the Hfi^hth ef ihti whole Pyramids

So the heighih of the wboU Pyramid.
AED,-'(wi!r'Ib8 found to be ?o Foat J [or
the greater Diameter AD is 24 Incliet,' the
IdfcfS; the'.difftrence'ifi. the Semi-dif-
ference 8, therefore UiaU ME lie jo foot ^
fof,- ■■■ ---i

Noi^MVing "found the heighth of the-
whote Py»lnHl f6 b^;? Pe^,'.rj4irr«by-fiBd'
the*fcoh(efit of 1hfe^w*«(fe^ffyt9iriid-to'be 4a:
Foot^.thriv'in ihelefferPyralV^ BCE (here i*
giren the fi<ie of irs.Bafe BC ~ 8, an J its
lengrMEib Aictwalfof-'EW 30 — -IMso
"ait JE^j*, ifo 'I "SiWl thfr CtAii Content oif it

'-'•■■ book

99 The T^g Sarv^or*t Gmtl^
from 40 tfae coDtent oFthe greater Pyra-
mid there will remain ;8. %'2 Feet for dl»
fode folid Content of the Fniftrum ABCD.
After the fatne manner ii found the fb-
lidity of the Frufbum of a Coor> And this
W atfo ufeful ID nKafuiitng of Tapering
Timber, Round or Square, and for findiog
the Liquid Capacity of Bccwcr&Cmical, M
.pyramidal Tunc.

Of Meafiiwig Jrtifcert Warh

Becaofe moft, if not all W^orkmen in ca^
ing up their Dimenfiooa y make afe of cro&
Multiplication, I think it wtU not b« am^
to give you an Example, (V twaof it, be-
fbre I enter upon their feve^al nK(hods of
oieafbriag their Work.

Note, Feet muUip^'d by Feet produce
Ftet i Feet by Inches ,piodtu:e Fiet mi /h-
ebes s and Inches by Incbo^I^odQceJbcin.
Moi.tvelftiu of hebes^^

Feet rncbes^ .

Therefore (»- awkiply %^%/^^
by 4.zSw3'
PiiA nujlttply the, Feet by the 12 i. o
Feet and the piodo^iv 12 2112' 1
JFdet, thearaoltiply crob^w^e o.:^

- Feet by Iflshes, ofs..4vby.tf 14^10.4-
-which; makes s^ilpches or 2 £!«4t and :} hy
3^ whkh aalix^ 9 iqcbei. ^-S^t Molty^y

T^e T^ung Surveyor s^ QwJh. Fgi

dw Inches 6 by ^ and the produQ it iS
twelfths of an Jficb, or i- 4- lothi ^1 whicb
produfb fet down and add together^ at.iii

ihe Operation

Mrt Eiamila.

4:2:
l;8:
0:1:8

7a : ot
S : 0:
3 !«:
0. :. 2:11

37"^^*

222 : 00 .
1 :
12 ■■ 6
': : S

55: 11:8 .1 80 : 8 :|i 235:^:*

Kr^j Glafier* Work^and rab*dand gav^d

Brtck-work are meafur'd by tluFoot Sqiiarr..

Example

If a Window be 6 Feet 6 Inchei high and

3 (eet 4 Inchei btoad ) how many Squai*

Feet of Glazing is there. ^. ai : 8.

Stcmify^

90 The Toun^ Survejfcr's Guide,

Sicottihf, I^inting, Pariag, Pla&tii^,
and WainflcDting,are mufur'dby theSguzre
Yard.

ExJmpU.

If a Ceitin?, be i; Feet broad» and 17
F<;et. 4 lii JbDg,'lKfur;.}naiS7 Yards doth it
ccotaia^ .A/I 21 !X^rdsi^

, - n-V'^ ■ ■

321 .0

25 :
Tiirdfy^ IVtine, Raftering, and floor*
iag meafui'd b/ the Squaie, contaiaing zoo
SqaareFeet

If a piece of T^Iii^, be 40 feet long

Bfid 1 3 Feet s lachet' broad : How many

^uares are (here in it ? 4nf- 5 Sq. 36 Feet.

.. ■ f

Square

The Tou^g Survejfor^s Guilte. g i
Square Feet. 40"X7"o

• S20 :
i6:

'■'■■'/■'..■' S3i5,:«,. ■
Foarth^t ComjpenSiUk-work'ii mea-
far'd by the Square Kbd,,. containing 272^
Square Feet ; But i£-lll£.JB''jIl be not one
Brick and half thick , , it miifl be reducf d
(0 that Standard, by ^liis General Rulfv
Multiply the Sipei-ficial Content of the
Wall by the thieke«fft~-thertof in half
Briciit i divide that pnodD^ by 3^ and il
gives iht true Qpantity* ''

If a Brick Wall that ia^U Pppt-thic^
be 40. F^et loofe^, ind 9 Feet 11 tnchea
higb. from .the roiindatibn, it ■wiUeimf
tain xRod" i.Qu.jf^/Feet, ."

■ I 124:5 1

Exanu,

S*j Tbfi Toung Sunirfer*t Guide,.

If a Bricic Walt i Bricks tbidc be f
F«t 6^ jiKhei in length, and 14 Feet 9
Indin in breadth ). the true ctHitent after it
ii reduced to the Standard, inz, i, Brid^
» ) Rod, 2 QusftM-«i 40 Feet.

700 : o
37:6 ■
7 - 4

_ . 744 : »o
Kumb, 4- Bricfci 4:0" . ;

i)29-j9 : 4 (99 J

Whidi dm^ by "o, 272T, giv**
3. Rods 17^. Feet : Which ia the tnie
Content of the Wall. , , ,

A^. B. The Bricklayers have a naiticu-
larwayof mcafuring Chimneys : Which ir
by multiplying^ the Girt of the Chimne^i
ty the heighth thereof, from the Foundati-
on to the Hearth of the next Chimney »
jHld the thjckneA of the Jams ii taken for
its thicknefs % which method they follotr,
till they come to the Shafts.

/^nd Ihofe thejf fiiit for the length of a
Wall, the heighth ctf which is the heighth of
the Shaitt and the thicknefe always two
Btickav ^«"Vfc'

The Towig Si&rveyffr*s Guide, ^|

' BxampU.

■ If a ChinlPey be 24 Feet 3 Inches abwit,
its Heighrh 9 Feet f Inches, and the thick-
nefs of the Jams one Brick and half, what
will he its Content? Jfif- o Rod 3
■Qu. 24 Feet.

SI6

10

a

^

I

228 : 4. J«f. in Feet*

7S«s, ThiM they meafure theChimneyi
of every Floor till they come to tiw
Shafts.

If the Girt, of theOiimney Shafts be
20 Feet aQd the heighth 1 2 Feet 3 Inches,
hour much is their Content ? Jup o RoA
3 Q."' 4^ Feet.

2o"^i^o

3+0 : o

S •• o

fbe

e4 Ti>^ Toang Saneyor's QctiJe,

The meaforiDg Book ought to be divid-
ed into three Colanmt ( <u tbt Exntple
Jl>£wi ) in the firA, the Kames of the Dt-
roenfioBt are f«t dowD, in the ftcoDd, the
pimeDfiont themfelvcs, and ia the USr thf
produd of thofe Dimenlioni.

After you have takin, and fet down the
Dimeufioni; Your next work* i< to maltipjy
tbem upon a wiAe Paper, and fet down
their produ£h over agjinJt tbem in the
fecond ColuoiD : At-ysaotyiW in tbe
Gample.

JKnut

^The TaiMg Svrvej&i's Guide. f^
N.imcseftheDm. D'mmt TidrDrtJttBs.

FheGiriof ihe>
4n<I«ioD:WalJ (
King 4 limc*^
Thicknefs. , ^

FheGiriof ihe;j
F0w<I«ioD:'
abating

its Tiiic .

Thf Heighrt.

Chimneys Girti
Hdghih twice.

Windows deduce
three limes.

Door dedai^. ■

Girt upper Wall
Heighth.

Chimneys twicr.

..'^JB4tiws4edtlc.,
: 7 liaie*.

Chimney Shafts
4viccb ■

F. In.

3f>tO
I2;o

7:0

115:4

2^:0
9:6

i7-,o

i:6

12:0
410

= i384,Feet.

liB
= 624, Feet.

tiB.

= 73 F. S Id.

t iB.
= 28 Feef.

li B.
=149^4.111.

iB.
= 494 Feet.

it B.I ' .

='i7lF.«In.

.2. B;

?= 96 Feet.

Kow

9*

Nov to cad up
llwir Dimeofions:
make 4 CtJamns,

8sinthrMargin,in
thefirftsf Which
patall theprodu£t
•Fone Bride and
half ThicJcnefr '
that are not De-.
dufliom, ir there
be any of 3 Bricks
thick put it dovn
twice, efc. thrn
pat downaU «•
cept ^edu£iioot,
that are oneBrick
thick^iftwOftwice
wdiffoBlyhal^
as in tfaeEzaoi-

tBr.
F.H.

3907-4
a7j;2

1 Br. imr. i.m
F. F. Id.
4«:o „,«

9A0 I7i:tf-|

(S8rf:o 373:3

J254'"'
4S7H

R. Q. F.
= 13 am'

. -■; ,_ 1

3> 378(457
•a*

iI7!3!««.o)(i3.
»73

Then aii up the £rft Colamn, from the
'Sbqi of which, l{ibllra£l the Sum of' the
•Column of Bfick M(thalf DiduaionH al-
fofromlhe Sum of the fecond Column,
fubfiraa the Sum of the one Bride DftJuffi-
ons, pf tbm It mif^i^lhcu tedxKe the Re.
mainder to the thicknefi of a Brick and
ilali^ and add • that rcfult to the Remainder
of the firfi Column, which gives the Con-
«nt of the Brick work in Feet, and the

B'

Tl&f Toting Surveyor's Guide. ay
Rods are found by dividing it by 272 i
As plainly appears in the Operation.

The Art of Surveying and Mea-
furing of Land.

Fhjl of the Chain,

Ecaafe Mr Gmter'f Chain is nwft in xtte
) among Surveyors for meafuring of
Lines, I ihall diiefly infift on ihat Mea-
fure, it feeing the beft in tife for Lands.

This Chain contains in Length 4 Pole or
66 F«t,, and is divided into looL'nks,
each Link is therefore iiiLength vl^^inchej:
If you wouW turn any Number of Chains
into Feet, you muft multiply them by 66.
as !oo Chains multiplied by 66, makes
6600 Feet ; but if you have Link's to your
Chains to be turned into Feet and parrs oJF
Feet; you muft fet dbwn the Chains and
Links, as if they were one whole Number,
aiid after having miikiplyed that Number
by 66, cut from the produia the two laft
Figores to the Right Hand, which will be
the Hundredth Parts of a Foot, and thofe
on the Lefthand the Feet required.

Example,

jSj The Tom^ Surveyor's GuiJg*

■ Example. ^ .. /.j .;■

Let it be required to know how many

Feet there are in 15 Chains 27 Linkf.

I fet down tlius the Multiplicand 15,25

Th» Numbej of Feet ia i Chaiq, 64

Multi^tyer.' h— — 1^

.. ■■■■ : .- : ■' 9150

91 yo

Prodod in FmC. 1006J50 >

. ■ Tht Produft is roo6 ff^: Thii. it fo
fjlain, it needs do other Example.
. , Rut now on the <»tber haod, if ope tfaou-;
fdnd ttkd. fix Fee^ st)il an half was ^veii yout
fb reduce inioCf^ifie and Lifiks) 70U iinpA
divide ioo<S'yo by <S6, the Q.uotieat ^iril}
tie 15, 2J, */|l. If GhaioH 35 Ijnkp.

[b hk« inannuf, if. it had beeA aiJud,*
IjGW tn^ny PerchM b)^ been canrainedrio_
1.5 ehal^s £5 Lij^s, iyottiroaft ^ida-i^,
2-\ by 25, *h^ Linlfb in me Parch and th«.
Quotient Aofwers the Qtieflian. ,
^j.Vi5,25(6i. Aflfwer in Per^tec
.'i?o ■■ . '. / ..

'. '■"^5 :'/ "■'" ; ■■■■ '■' '-.:■ '• ■:

The Taung Surwyor^s GuiJe. 99
Admit I would know Kow many .Chains
are .contained in joo Feet.

. Operation.

38 Aftf. 7 Oiaios 57 Lia. ^y-

tg Meaftire* .

ftjches

Feet. ''

66q\ 22o[ ■
28o!l76c1 j:

;2o I g^o 220I 4° Furl. i ■
S,iiio ;28o|l76c1 i 2o - .8 IMilk

P 2 . '' A JaUs

4

-leo

S 3.

The ToUng Surveyor's Guide,

S

1

>

-57

3-

§ §

O °

^

IJ>

1

1^

1^

'

1

?

1

1

i

I

1.

W\

The Toung Simjeyor's GitiJe. lor
The cooimon Meafure for Land is (he
Acre, Vtiich by Scatute is appointed to
contain i6o Square Perches^ and it matters-
not in what form the Acre lyes in , (o i«
contains ]uft i6o Square Perches : As a P^-
randogram lo Perches one way, and i6
another contains an Acre-j To dees 8 one
way, and 2oaiiother, and4.one way and 40
the other. If then, having one fide given in .
Perchsyou would knownow far you mufl go
on the Perpendicular tocut off an Acre, you
muft divide 160 (the Number of Squ-ire _P.r-
cbei in at Acre) by the given fide, the Quo-
tient is your Dfirc. As for Example, tlie
given fide 20 Pe;che8. ■ Divide 160 By 2o
the Quotient is 8, by'this I know that 20
Perches one way, and 8 another,including a
Right-Angle will be the twofidesof an-Acrer
the otlier two fides muft be parallel to theO.
And here 1 thinit: it convenient, to infert
this necfffiry TiIjI"", fhewing the L-ngih
and Breadth of an Acre in Parches, Feet .
and partS:of a Foot .• But if y oar given fide
had been in any other fort of Meafure^ as
for inftance in Yards yon muB then have
feen how many Square Yards had been in
an Acre, and that Sum you muft have divi-
ded by the Number of your given Yards,
the Quotient would hare, infwered the
QueflioD. '

F 3 Breadth-

lo^ The Tcufig Snrviyor's Guide^

2 Length of g Length of
& aoAcre. Si an Acre.

!?

•9

'^ •□

s

3-

??
?

1

S

?

«•

lo

Ill

.0

28

5 II i

II

14

9

29

7 01

la

•3

5t

?o

5

f i

>3

1_2

5tt

3]

'I

2 Y

'4

II

-i

i?

_5

!^

10

II

33

4

-il.

i6

10

_i

ILi

17
18

9
8

14,1-

3!

36

;4
4

9 t!

7-7

i^

8

_#j-

37

_i:

5 t

20

8

IS

4

JJ

!i

_7

lOrf

.11

j4

Jlj:

22

.7

4-7

40

4

"6

■H

6

1;^

£r

J

i+ij

2 +

6

11

42

3

13 t

2';

6

j3

43

J

iiU

-

26

J

27t

44

3

■*o t

27

5

i!t

4S

1 ?v

"-

^

■Ea'

The Toung Surveyor's Guide* loj

Example^

If 24 Yarfs be g/vea for (he Breadth^
"ho^ many Yards fhatl these be id length -
of the Acres.

, fi^fi^ I find tbat an A^re contains 4840
Square Yards, which I divide by 24, rhe
Quolient is 201 tr for ihe Lengih of the
Acre" And thus knowing wilt how to fake
theLengthandBreadthof an, Acre, you may
.al(b by the fame way know how to lay
down any Numbef of Acres togelher.

Reducing of one fort of Square mearure
to another, is done as before ta^ight in Long
meafure by Mnlti plication and Dl'vifion.
'And becaufe Mr Gmtert Chain is chiefly
ufed by Siirveyotg, I ' fliall only inflanre in
that, and fliew you how to turn any Num-
ber of Chains and L'nks into Acres, Rods
and Perches : A'ute, that a Rod is the (onrih '
,'pirt ef an Acre,

■ A-n3 fifft mark well ihat 10 Square
Chains make an Acre, that is, to faj', one
Chain is Breadth and lo in L-jigth, or
2 in Breadih and jr iii'Length, is tlie'
Acre i as you may fee by this fmall
Table. .

1 04

n

f TS

3-

3

ET

w

El

a

I

2

3*

2

»

?3

3

■*i

4

5
6

31

3

66

?

7

>

5

23

9

11

71&£ TTwnj Surveyor's Cuitie*

And thus welT weigh-
ing that 10 Chaini
make one Acre, if any
Number of Chains begi-
' ven youto turn into Ac.
you maft divide them
by ici, and the Quo-
tienf will be the Nim-
ber of Acrts contained
ID (o many Chains.

But ibis Divifion, is
abbreyb^ed hy on-
ly caiting off the laft
Figure, as ir 1590 Chains were given to
iiitointo Acres, b/ culling off the laft Fi-
gure i^^.'o, there is left 159 Acres, which
is alone as if you had divided lypo by la
But if Chains and Links be given you to-
gether to turninto Acres, Roots and Perches,
firft from the given Sum cut off ; Figures,
which is 2 Figures for the Links, and one
for the Chains, what's left (hall be Acres.
And to know how many Roods and P.-rches
are contained in the Figures cut off, Multi*
ply them by 4 from the produfl, cutting "
off the 3 lad Figures, you will have the
Roods ; And then to know the terchef,
multiply the Figurees cut off from the Roods
by 40, from which product cutting off a-
gain 3 Figures, you have the Perchis, and
the Figures cut off are a Thoufabd parts of
a Peidi.

Tie Teung Surveyor's Guide* 105

Example.

1599 Square Chains, and yj Link*,
bow tmoy Acres, Roods and Perches.
Acres 1591 555

_t '■'■'■
An/. 1 59 Ac. 3-Roods. Roods i\% 20.
32 P<rches. 800 40

1 000 Pdfches ?2l8o3-
On the cooirary, if to any Humbtri ot
■ Acres given, you add a Cypher, tliey wifl
be turned into. Chains, thus s>9 Acres are
S90_ Chains, .100 Acres looo Chains, £?'r.
the fame as if you bad multjplitd the Acres
by 10. And if you woultt-jarn Square
Chains into fguare Links, add four Cyphers
to (he 'end of the Chains , ff> ^ill ' $90
Chains bs 9900000 Links, looo Chains
1 0000000 Lrnlcs, all one as.it you had-
niultiplyed 990 by loooo, the Number of
Square Liiiks contained in one Chain.

And now , whereas in Cafting up the
" Content of a piece of Land mea(ured by
MtGmtcr^s Chain, viz. Muliiplyiog Chaios
and Links by Chains and Links, the pro-
iuH will be Square Links ^ you muft there-
fore from thai produ£t^ cut o^ ; Fi£urei
to find the JVfres j which is the Tarns as if
Toudividtdthe produ^by looooo.iheKum-

Fs ^ to

I off The Young Sarveyor'i Guide,
ber of Square Links contained in one Asre,
tlien mtilriply the 5 Fi^ores cul off by 4 -,
and from (hat product cutting off 5 Fi-
gucffi you vriW fave the Roods. -L'*ftl}\ .
Multiply by 40. and lake away as betoce
% Figurei, the teA ire Perchet.

A4mit a Parallelogram,' or long Sftiare,
to be one way ; Chaini 57 Links, and ibe
sother way 4. Chains 35 Links: l demand
^ ihft content in Acres, Roods and Percfcw.

Mnltiplicand. ■ 1 ^55

Muhiplicator. 4^;.

'A<nf. ya Acres. ^ . 2775

J. Rood. C 2220 ■

3fi Perchflfc \ ;Acr<s-2|4i42;
■ ■ ' ,4

And T-rr P^f's of ■ a Perch.

PeKhes 2<5! 28 000,

QflnfirumenisandtheirUfe.

THjre are feveiral forts of'ChaiftS, as Mr..
Rathhotnt of 2 Perch long; Other jif one
Peich long'i Tome hays had them 100 Fe«t in,
Length :.

■TBiT^ung^ Surveyor's Guide, 107
l^eogth : Bdt that wjiich is inoft in ufe a-
laorg^ SorveyorX ^s being indeed the bell,
ie Vit Gimtett, which is 4pples long, co).~
UtniiJg jop Links, each Link b?ing 7i— J-
■fcDches : The defaiptionof which Chain yon'
have had already : Id this place I ^all give
von fixn^ fevr dife^tioos for the ufe-of it io
Me^urUg LiRt4? Ts^' ^^■'c that Uwy w]ikh>
^ty ^( Ch«io deviate not ftoma firejght
LisCf which yew may do by flaoding M
your InSrameiir, and looking through the
lights. U you fee them between you. and:
the Mark obferved, they ^e in a ftreigh*
X^ioe, otherwire Dot. Bnt wiljiout.aU this,
irooblfl,. they ro»y carry. (|ie Cbain friie
enough, if he that follows tlie Chsio, al-
ways caufes him that goes before him to be
in z dve£t Line betveen himfelf and rhe
place they are going tOj fo as that Jhe" fore
,. Man may always cover the Mark from.
him fhatgoes behind. . if they (werve frotn-
Ihe Line^^they will make it loijger than
really it fs j a flreight Line being (heneareft -
diflaflcethat can be feetween any 2 places..

Bi fqre that t he j which carry ihe Chaih
miftake not over or under in tbtir A^-connf,,
iat i1 they (hould, the the Error would lid
very cnnfiderable^

But the ufual way fo prevent fuch jmt- .

takes is, to be providwl with KiTmall ftitk*

3(bar£*d at one tfndto fiick in the Gfound^

,- an*

„ . Goo<;k- -^

ipB The Toung Surveyor's Guide,
and let him that goe§ before take all into
his hand at fetting out, and at the end erf*
tvery Chain ftkkdown onej which let him
that follott's take up, when the lo flicks are
dpne,"befu« they have gone lo <- haio«i
then if the Line be longer, let them change
the flicks, and proceed as before , keepirg
ID Memory how often they change. They
tMy either change at the endof loChaiur^
iheii the hindermofl Man gives theforemoft
all his fiidcs, or which is Utfer at the end
of It Chaini, and then the lafl: Man. muft

five ihe &ft but 9 flicks, keeping one to
imfelf. At every change count ihe ftickg,
for fear yon have dropt one, which fome- -
-times happens.

Of Injiruments for- taking of an Angh
in the Field,

THERE are but two material things
to be done in the Field, the one is to
Meafure the Unes, and the other is to mea- ,
fure Ihe Quantity of an Angle included by
ihefe Linfs j and the Infiiuments of the grea*
teft efteem, are the plain Table for finall
Inclofi'res, the Semi-Circle for Qiampaign
Grounds, (he Circumference or the Theo-
dolite, i^c. To defcribe tbefe lo you, their
parfB, how to put them together, take
4hem afuoder, i^c . is like teadbirg the Art
- - of

. TheTdung Survey&r*s Guide. 109
of Fenring fay Booki one H:ur8 nfe of
Ihem, or btit looking on them io the Inftru-

ment-mitkiTs S^op-, will ' better defcribe
the 111 to you ihan tbeReadiDf;oneHund[cd
Sheets of Paper concerning them.

To take the ^latitity of an Angje.

Fig. 84 Let AB and AQ be 2 He%»
of a Fi^ld, to'£nd the qi^aoticy of the-
Argle A hy the plain Table.

Phce the Table as oigh to (he Angle A at

?ou can, the North end of the Keedlc
anging dired]y over the Flower de Jjict^
then mikt: a Mark uptm the Sheet of Pa-
per at arty conftant place for the Angle A,
and lay the edge of the Index to the Mark,
farnirg it abbu% till through the fights you
efpy b, then ^raw the L'ne AB by the
edge of the Indei. Dd the Ume for the '
■Line AC, fceepng the Index ftiU upon the
filfl Mari:, tlien will you have upon yoat
Table an Angle equal to the Angle in (he
Field.

To tahthe gomthycf the fane Jiggle Bj tU
Semi-C'tcle,

Place your Sfmi-Cifcle in the Angle A,

~a< near the very Angle as pcjfibly you tuq^

and Canfe Marks to be fet op nigh B aod^'C,

fo £ar oS the Hedges, as your InfiruiBeiit

at

at A fiands, ih«D rum tbe Inflrament a-
bbtrt fill throDgh the- find fightt ypo fee
the Mark at B, there Screw it (aft j neK
tiini the moveable Index till ihrongh the
fights ther«(^ }>q9 («e the M'tk at C, and
fee what deg. upon the Limb are cut by
the Index V which let he 47, fo much is the
A'glc BAG.

.' Hij* totaki iyefjiht. ^fhvCiretimferetitor.:

^X9 your Inftrument as befoce,- with
riie Ftovwr de Luce iosratdt^you , then
direft your Sight! to the Mark at E, and
IH What degre«i aM:iheit cat by tfle Soirifa
end of the Needle, irfach let be ^^y dothe
Xami'to the Mark at- C; aad letthe Needi«
tfiere cut' 100, Sobftrad the Itffa out ot iht
greater, and ^e Remainder is 4;, the Afigt*
rt-quired. IF the Remainder had heen more
then 180 flegrees, you niuft,ihen haye ftil-
Hraaefl it out of 360, the lafi: Remainder
^uld l^e - bem the Angle defined.

£bw hy the Semi-Cirde to tah the ^anthyof
'an AngU in the 'FisU hy the A«dJe,

Screw faft the Inflrumetit, the North-end
i<(ff the Keedli- hanging direSly ovef the
'Slower de L«ce in the ' Chord , turn the-
ilndei abouf, till- through th 3 "Sights you
f£7 the Mark at B^ iind aote what dfgree^.
tha: .

The Tmrng Smtepr*s Gidcte, i n-
the Iniex curs, which' let be 40 ; move a-
gain the Index to the Maik at-C, and mm
thed^M cur, viz. 55, fobflrat^ tbe lefs
from the greater. Remains 15, the QuaO-^
tit/ of the Argle,

Note, If you mrn the Flower de Luce to-
ward! the Marks, you mufl look at the
l^orih-end of the Needle iot ydat deg^es.
^od the Eaft and Wffi pokftB are matkecl
contrary, viz. £aft with a W, and WeS
with an £, beciufe when you turn the In-
Arument to the Eaflvard, the end of the-
Needle will hang over the Wefl-fide, fcJ'e,

If by this way oi Jiiviiiaa of the Chord,
you itovld takp the afprefaid Angle, direft
tint la^tument (fo ^^ Pknrer m Lme from
fou,) till through the Sights you' efpy the
Mark "at B ; then -fte w h a t d eg rees -are cut
by the North' end o£ the Nedle,.. which
let be N.£,44; next direct the Inftriiment
to Q and (Tie Nirth-end qf thf Needle will
cut N- E. 89. Subftrad the one from tlii
'other, and there will Remain ^^j. for tb^-
Angle. ■.■■'',

'GftheVieU S00I ' "

Too muft always have iit readinefi in,
jhe Pield, a little Book, in whi^h fairly, to
ipfertyour Atales'and Lines s wliitjh Btiok
you may divine by l.inea into Crfuinns ,
K YdU Ihall ibink, couvenieftt in your
Ptaajca

113 Hie Teuag Surveyor' t Guide,
Vti&xce^ having always a large Columa
to the Right-hand, fo pat down remarkable
thing! you meet with, as Brooks, Mills,

Example.

If yoo had taken the Angle A, and found
it To contain 4? Degrees -, and ineafured (he
Line AB, and found it to.be 12 Chains
;; Links, fet it down in your Field Book
ihcs.

A deg.|MiD.|Gl>.|Lia
45 1 00 1 12 1 2!

1 1 .

Z.(tjilj, You may chufe whether yon vriH,
have anjr Lines or not, if you can write
flreight, and put the Figures diredly ont
under another ^ for this I leave to your own
fancy i for I believe there arc not two Suf •
freyon in Enghndj that have exadiy the
ikme Method for their Field Notes-

Oftbs Scale,

Therfr are feveral forts of Scales, fame
larg", fome fmall, according as Men haw
occafion to ufe them, ior the laying down
C lalna and hinks } ^fo you have «pun

The TmngSurviyorsGutd*. 113

the fame Scale Lines of Chorda, for laying
down and Meafuring of Anglts. 1 :anno
belfer-eiplain the Scale to you, than by
fliewing the Figure of fuch a Decimal Scale
as I think mo^ ufeful, and are commoalj
.fold in Shopa.

Of the PrttraSor.

The Protraftor is an Inftrument with
which, with more eafe and eiadlntCs you
may lay down an Angle of any Number
of Degrees, tlian you can by the Line of
Chorda : And when ynu have Surveyed by
(he Needle, by pacirg the Diameter of the
Protrador upon a Meridian Line made up-
on your Paper, you readily with a Needle
upon the Arch of your Protraaor, 'ptjcfc
' oiTthe true Situation of any Line from the
Meridian, without fcratching the Paper, aa
you mud do in the ufe of the Line of
Chords. It i> made almoft like, and gra-
duated altogher like the Brafs Limb of a
Semi-Ciicle, performing the fame upon
Paper ,- m your Infbument did in the
Field. , .,

Haw to lay iuvn an. AKgU with tb« fVc-
traSoT.

fig. 8y. If it were required by the Pro-
traaor to lay down an Angle of 36 deg.
Draw

it4 TZ>^ Tffung Surv^or*s (juiSe,

Draw ibe Line AB,_then take the Protraflor
and putting the Needle through the Cetitei-
p()int thereof, place the Nwdle in A, fo
that the Center of the Ptoiratlor m?i^ ly^
^'uft upon the Liwe « A, move the Frc-
traflor about till you find the Diameter
thererf lye upon ihe Line AB; then at ?o
degrefs upon 1(15 Arch, witli_your Proirail-
ir.g Needle make a Maik upon the Paper,
as at C, draw the Line CA, which (hall
make .an Angle of qo degteej , viz^

BAG.- ;

tiov to Jay iotnt the 'Angle "by tbs Line of
Cbordi.

Fig, 8(S.If it wrTc Tequrredto mafre aft
Af^glethatfliDuldcontain 4.5 tjfgees. Draw
a Line ar plearure, as AB j thtn fitting one
Foot, of j'our Compaflis at' the beginning,
of the Line of Chords, fee that the other fall
juft upon 63 D.greesi with that eitent fet

Diie Foot in A, and defcrite the Arch CDj
then .taftfi from your Li^e of Chords 47
degiTK, and fetting one F'^bPi'n D, make a
Mark upon the Arch at C , (hroigh R-hich
draw the Line AE i fo (hall the Angle EAB

■ be45degreej. If bjiheL'he of Chords you
would ereil a JPerpendirular Line, it is no
more but to jnike an Angle that ft)all coi>
'tain 96]t)fgrefS. ^ ■

;■■ ;,-■ "•■ ■ ■ ■ ■ - .- ■ •The.

The Tirnng Surveyor's GuiJe. x 1 5

The rea&iO why I bid you .take 60 froiil
At hiao nf Chcads to. make yaw Arcli by,
is becaufe 60 istheSaJni-diatnetri of h Citcit
vioU Gircanifereiice is ^6o-

• How to ca(l up the Content of dfigufe,
the' Lines being given in Chains and
Links,

HAving defciibed ihefe plain tnftrunwnts*
and in fome me^fuie {hewed the tfCf
of them, I intend to (hew him, i; How
he ought to make his Computations 1 2. The
Groands or Principles that will jufiify him
in fodoing. --

For thfi ^irfl takt thefe -Ek/mj. ..

-I. Pat ■down your Length .and 3readtFi

- of Squares and Oblongs , and your Bi(e

and t Perpendicular of Triargles "direftly

-under one another, eipreilid by Cliains and

Links, with a prick betwixt them.

2. If the odd LiuJu. W££e under 10, put
3 Cypher before the Figure^ fiprefling them
as Chains and Links ^ arid if there be no
odd Links,' but alI«v«H Chain?, put two
Cyphers after the prick,.
* ?. Maltiply Length by Breadth, and
,Bafe by i- pBrpindTnriar, -according to the
Rules forfioding the Gentent-of Figures..

4^'

xi6 The Toung Survejfor*s Guide.

4, From that ptodu^ cut off ; Figurei
reckoned from the Right-hand badcwards .
with a dafli of your Pen, fo flial) thx^ on
(be X-efthand be Acrep.

^. If thofe on the Right-hand ureie not
all ; Cyphers, multiply them by 4, and
cutting 0^; toirards the Right-hand zgiin,
the reu on the Left-hand will be Roods or
Quarter*,

6. - If amongfi thefe <; Figures towards
(he Right-hand that were cut or at the fecond
Mulriplication, there be any Figures befides
Cyphers, multiply all the 5 by -jo, and cut-
JBg 5 again w'th 3 dafli of ym:t Pen, thofe
00 the L;ft-hand are Square Parches.

ExampU I.

What is th« Content of a Square, whofe
fidei are every one of them ^ ;o Lio^t-
Length 4, jo
Breadth 4. %o

22500. /

r£oo

210 2500
4

1 oooo .

40 A'if. t Acres and 4
- — '- "' Perch, as appears.
4I00000

Exatpfle

The Toung Surveyor's Guide, 117

Exa$apU -II.

I-ct-a long Square, whofe Length is 14
Chains, and B t-adth 6 Chains and 5 Links
what is the Content > ,

Length, 1 4. 00 -

Breadth, 6.0$

70C0
, 84000

8I47000

'' ■ ' "-J^/ 8 Ac. I Rood,

. ;il47Coo 35PeKh?8,.asthe

40 work makei evident.

35{2ooo(i.
Example: HI..

Then h -a Triangle, whofe Bafe is 3
Ghains, and f the Perpendicular is 4y Lin.
what is the Contenr.

. The,

Ji3 Th''- Tomg Survtjfor's Gutdtp-
The Bafe 3.00
Half PerpeP' o. 45

IS 00

ISOO

A. K f

Atf. 0-0— 21

1 3 50.0
♦

540 oe- -

40

, aii^coo©

1 1 fliiU Dour demenAfate this vny of
caftii^.Bp a pifc«of.i.^nd-by the follow-
ing. SS^.

1. Itis evident, tti«tm<his way of Mul-
tiplication, the ptodoStis -Square Links -,
for every Chain being a Hundred Linki,
it is all one to .pulrifljy -4- Jo, by 4.50 or
450 without the Pricks, for they fignity no-,
tbing at ill in- OpmlioSi ' Tfac pcodu^
rh^4tor« of the fcft Eaunple wn -icAi
500 Links/ .

2. Every Chain being 4^erche« long,
it follows, that ; Chains in Length and 2
Chains in Breadih,- make an Acre, or 160
Square Perches.

3. FrorolKnceiit plainly follows farther,
that therC^ are eiaftiv looooo Square Lin.
in an AcEe^ for 5 Chains multiplied by 2, ,

it

• 7^_Toim£Surve^ar*s Guide, ^igt
ii the fame with ;oo Links ty 200, which
mafeea iQoeoQ; , Then according to theOW
" phia 'Kiile'irt- Aritfimeticlki 'ivhsn the Di-
Wftr cDnfiRs of 1 and Cy^hets; t^to^ioo^
iooo, looooo, f c.) cut off from the Rtghn
Hand fo many Figures of the Dividend aa
'rite DirtGkr'fc^X^fpfafrs, 'atd countiiig
them for the irsraains, i (o ihati tfacirtft ba.
tJjsMtffde le *he Qliotitnt. It- i*. plain-
then tiiat i.^y.'}c6 rqgaf& Links raxkes i-
Jictty ilod^75o6 fqgjir^ ^iolu over.

So I have iDad« it dear, ks farstctmcerns
Acrrst that the: Rules fprOHnpuutiDn arv'
good.. N(»w inr IRmidf aind'Pecchia,. it it
plairefrem rimtkneiifOi' Euii. in D.ciaial.
Acithinentcfej Multiply tbe giv«n Decimal-
by tbe Ntimter of parts in the next inferioBr '
dfoofniiialim, dsat-are cqu^Jo an Integer.
in diA'fame deaammation with the giuea
pBsimBJ^Bnd.ffe how. many .pjaccs arsiu the
*4^8di]tI;,Jinire-tban<*eraJB!liifc/giSien;Deci-r''
mal 5 and cut fo many off from the X'ifC--
fi»nd, jtAA'jfUafetFipansjB cmcff,- are the
vjiIae'«t.(WK)idI>cin3Bl.! So that ,tii:i way '
of caflifigupthe.Comeat of a (liece^f L^
is tnM'^ *i'.. '. ■'»■;' ■■' •■■ i . ■ .'' ' ' '

120 The Toung Survej'or*r Guide.

HoTo to meafure a piece, of Land, and
to PratraS it^ and to give up the
Content* t

AL L Clofes, or P<irce1s of Land, are
either fuch as need not to be ptotted
for finding out their Content-, but the Chain
alone dorS'the worlct or fuch as cannot be
meafured withont plotting or Protradion^
of the firfl fort are the Squares and long
Sqaares* and thefe, I fay, need no plotting, ' ,
for )'oa need only to niultiply the Chains
and Links oflhe Length,' by^the Chains and
Linkaof the Breadth, fo proceed as in the
lift Examples: Bilt all others, whether Tri*
angles or Triangulate, are to be protracted.
I ihall give Examples therefore in the- 9'
forts of Figures, Triangular, Quadrangular,
and Mutangular. Eut let me adviie the
Young Praditioner to remember tbef^'
things.

I. To begin at fomt notable Angle of
the Field, where there is fome Gate, Style,
&e^ Or if there be none, to dig up 3
Clod, or at leafi to obferve what Quarter
of the Heavens it pointerh toward, and on
your Pdper mark it with fome Letter.
- 2. To go Parallel to the fide of the Field,
accuftoming your felf to go' either with
jour Left-hand towards ihe Hedges, or ,
Contra

The Toung &trveyor's Guiiie' 121
contra wjih your Righc-band towards tliein ;
arid wlien yea go -con-triir)' to jo^ir ufual
Cuftomirioie it on j'our Pjper by (brae
initk known to" youi f*I^

3. To take heeJ, left yoQ contound
your I'elf by raking Lines off of Teveral
Scales, or mearudng Perpendiculars upon ■
itrrong ones^ for every Line of the fame
F^ure maft be made by the fame Scale,
and (he P.-rpeadiailarstneaftired by it.
- 4. To make life of a large Scale in fmall
CldTes, and of & fmaller when you meafure ^
great onei

y. To fet on your Chaini and Linki at
twice, when say Line is too long for youc
Scale.

Thefe things lielog pfeiTiifed, 1 proceed
thus :

Fig. 87. Suppofe ABC tobe a Clofe, be-
ginning at ihe Eaflein Angle A, and going
with my Right-hand towards the Hedgp,
I find the iid*a to be 4. 07, 2. 29, 3.4;-

I firft, with my CompalTes, take off (rem .
my Scale 4 Chains and 7 Links, and f?rtirg
it from A to B.'draw that Line for thxBate,
becaufeitis tHelongeftof the three; Then
I take 2. 29 off the fame Scale, and p it one
Foot of the Compafles in B, \ defciibe th«
Arch OK. N-'ir taking with my Compaffea
upon the fame Scale, the eitent of 3.4;:
I place one Foot in Hie poiit A, and Rjtfi
the ether make the- Arch PCi, interfeaing
G A

f;

J as The Totnig Surveyor's Guide*
the other in tlie point C ; and drawing the
L nes AC and CB, the Triangle ABC it the
Plot of the Field meafured^
K zt X muft find the Length of the Per-
endicular, which is done by fttting one.
'oot of the CompafTes in C, and eirending
the other to the Bife AB, fo as it touch and
pafs not over if; then the Leng-h of the
Petpcndicular is between the points of *he
CompalTes, and it being applied to the
Scale that the Triangle was made by, zi
appears to he" f Chain 42 Links i ivith the
4. whereof I multiply the Bafe AB, 4. C7,
and proceeding according to the Rule before
delivered, the Content appears to be o
Acres, i Jlood» 6 Perches, as is evident.

Hie Bafe 4. 07

f Perpend. 0-71

407 ,

2^49

28 8 97

.^ 4 ■

HI 5y8 8

6\2Z t2o

The Content of this piece of Lind may

be very leadil/ fouod without plotting

ir.

The Toung Surveyor's Guide. 125
' if, thus : Firft, Meafure the Bafe. Line A&,
then by the help of your Crnfs Staff, find
where ihe Perpendicular will fall from the
A'^gle C' upon the Bafe AB, wbith is al-
■ ways the neareft diftance itom C to the
Bafe AB ; and then meafure the Lergth
of your Perpentticular by yoor Ghaio, and
having the PerpgndicuUr and Bafe, you
know how to find the Content.

How to Miafurt a.^va^xayguUr or Foiir fdei

^ield.

Fig. 88. "Let ABCD be a four comer'd
Field: 1 beg;n as bclore at fome rematkable
Argle^ and gdirg round the Field, I find the
fides to be 9.04,8.75, 9.12,8, 17, and
the Diagonal AC 10, oc, I begin to pro-
tiad: iljus :

I firft, bythehelp of (hj* Scate arid Com-
palTes, draw my Diagonal 10, 00, from \
to C, and I.make a Triangle of it and the
firft and ferond fide 9. 04, antt 8. -j^, as
in the lafl Fitfid, and another after the fame
method of, that Dia,gonal, and the third
"and foruth fides 9. 12 ^nd 8. 17, fo have
I the Trapezium ABCD.

Then by the help of my Scal^and Com-
pafles, I find the Length of the Perpendicu-
lar of the Tliangle ABC to 'br ^. 90, and
of the other CD A 7. 2 J, which added To-
gether are 14 10, whereof the ^um 1*7.5,
G 2 by

1 24 The Toung Survejor*s Guide,
by which multiplying the Eife lo, co, and
proceeding as lormerly hath been ihewn,
I find, the Content o\ the Field to be 7
Act*»i oRoodS) 8Perchei, as here foltours.

The Bafe 10. co

y Perpen

l-°'i

5000

7000

7| 05000 . • ■ ■■

4

20000

40

S I oooco

Bor t» take fbi Hot 0/ «ij MtbanstUr

FM.

F/g. 89. Let the following Figure A, B,
C,p,F,E, reprefent a Field» <^ which, the
Plot is required. . i

fvP, Meafure the Length of the He^ge
AB 7 Chains, then Meafure the Length of-
rhe Fence BC 6 Chains ; ai alfu from A
to C the Bafe Line proper to that Xrian&le
which is foiind lo, oos all which Wute down
in your Field Book.

' Then

The Yoimg Surveyor' i Guide. i-^.

Thn Meafure the fecond , Triang[le ia .
the fame Order, beginning at C, and Mea-
furing to P, which is found to be 3. 10 «
-then Meafure from C to E ;. 1;, and Iila-
wife the Bafe Line C E. 8. 00, which put
down £or the fecond Triangje.

Then obferve the laA Triangle, which is
an outward Ao&le, and muft accordingly be
Meahired on the out-fide of the Field, and
fo qoted down in your Field Book v fo the
Lengih 6i the Lin.- EF 2.15, and AE j.8o,
ihe Bafe Line, and AF 4.00, all .which en-
ter in Tour Book as follow^.

F/Vjf Triargle ABC inward, 2, Trijinglp

CED inward. .

,G

L

C. L.

AB

7.0Q

CDjdo

•EC

6.0c

»fi!.i!

AC

0.00

C E 8. 00

• — —

Third

Tiiangle

AEF'««wiid, :

c..

L.

EF s.

IS

F A I.

06

iAE!--

83

Haw., tt Prolr^3 the former Work ttpcH Pjftr

FirPj Draw a Line upon your Paper ae
pleilTure, as AC, and take from^our Scale the
Length of that ^ine, lo. oo ^ and ftt it
' G 3 from

I Q 5 The Toung Surveyor* s Guide,
ftom A to C i then take ftomyour Scafe the
L -ngth of the' Line AB 7. eo, and put one
Faot of your Compafies in A, with the o-
ther defcribe the Arch t a ; then take the
L'ngth of the Line BC 6.00 from your
Scale i placing one Foot in C, with the
other crofs the former Arch in B, as bb,
this done draw the 2 Line* AB and BC.

S*co>ti, Take from your Sctle the- Bafe
Line CE 8.0a, and placing one Foot of
your Compafrfs in C, with (he other de-
fctibe ihe A^th ee, then take wiih your Cem-
pafTs the Length of the Safe Line EA 5.80,
fetcing one -Foot in the point A with the
other crofs the former in the point E, a»ff,
which point' £ is the meeting A) gl^o both
the other 2 Artg'es.

Thirilf^ Fir the protraflionof the Tri-
angle CED, take f^om your Scale the Line
CD^.-io, i^acing one Foot of your <!;om-
pafTe* in C, snd with (he other -malee the
A-'ch cc, then take the Length of the Line
DE 5. 15, and felting one Foot in E, with
the other crofs the former at D,as dd, from
which lnt£if.dion draw the 2 Lines CD
and DE.

L^ftlys For ihe Triangle AFF, take with
your Compaffes EF r.15, ] bring tjue Foot
of your Compalies in E , with the other
ftriks the Arc ti hh, then (ake AF-400, fer-
(ing one Foot in A. and »vith the other crofs
the former Arch inF, draw Lines therefiom.

f;oosic

The Tput^ Surv£yor*s QuiJe, 1^7
9s from A 10 F^and from F to E, foliave
you protra£ted jour Plot upon Paper, as
was ff quired.

And you jnuft he careful to note down
theSdruation of the AngUs, r»«. inward and
outu^rd, for fear of oommit^ng of a mi-
ftake when you protrad the fame.

Now if you draw aLine from C to F,
you divide it into 2 Trapeziums j, and then
the Content is found as hath been before
taught.

Hav to fake the Hot of a F'uU. by g^iitg
romd the fame.

JFig.ApLit ABCD-reprefent a Field to
be meafured. Firft beginning^ at the. Angle
At I meafure one Chain iti Length towards
B, 86 to q, and another towards £ as to b $
next, I take th? diftance from a to b i, 50,
-and note it down in, my F-ield Book, t'of '
the Quantity of the Angle A \ and nieafure
the Hedge i^B ;. 00, and put it 40 my Field
Book.

Ke« Icome to the Angle B, agd mea-
foring one Chain tod, and another to c,
I take the digance d c with my Cliain, and
I find it to be .1:. 40, and the Hedge BC 3.
1 5. Next I come to the Angle C, and niea-
furir^ one (. hajo to e, ami another to f\
and ■ take the diHance f e, t fjnd ii to be i.
ic, and from C to D, 2. 17, and fo, I pro-
G 4. ceed

>»3 The Toung Surveyor*: Giade,
cefd till I come to the Angle A» and I find
to be ai follows.

C. L. C. L.

A I. 50") f AB .3. 03

B 1. 40/ ■ \BC 3. IS

Angles

C I. io>S;drt /CD2. 17
D I. 8ol^ )DE2. 80

E 1. 39J (EA2. 60

How to Ptotroa the former Jf^otk.

Tirfi, I take from tny Scale I Chain, and
having drawn. a L..;i a> AB, upon A as
a Ceuter, I ftrike ■^=^ Arch a b ; then take
from your Srale 3, r.j, and fet it from a
to b, and draw the L'ne AE, fettirg thereon
?. £0 from A te E, and j Chains from A
to B } then talcing one Chain from my Stale
■and putting one Foot in B. I ftrike the Arch
c d; neit I rake 1 CKain 40 Ij-nks, the Q,uan-
tiry of the Angle B, and fet it from d to c,
and draw the Line BC , making it to be
in Leni^th 3. 15. Nsit I come to the
'A')g!e C, and fetting one Foot in C, wirh
the other I defcribethe Arch ef, then tak-
ing I. 10, from your Scale, I fet it froffl e
to *, and through tlie point f, I draw the
Line CD in Length 2. 17. Nextl'cometo
theA'g'eD, and always taking I Chain -
from my Scale, [put one Foot in D, and
with the other defcribethe Arch on % xh<sa
taking

The Toitng Sttrvejor^s Guide, 129,
taking iChaio and goL'ofcs,! fet it from o to
n, and the Line DE, which Line muft juft
meet the end ot the L^De AE and contain
in Length 2 , 80. if your Work be well
done.

I uiuft acknowled^ that this fort of Plot-
ting of Pdr«!s of Lind that have many
A' g'es,Teqnires not only mors care and pinsj
but; better Skid and Memory than to draw
Diagonals upon Paper, when the Plot is al-
ready taken by theplain Table. I Ihall there-
fore give you fome ways to help yoor felf, ■■
fo as to be oDt of danger of Mifnkes.

One way is, to divide aMnltangularField
into 2 or more parts, then might each part
be meafured feverally, as if they were ft-
veral Mens Lands parted by a Boundary.

Another way, which much helps the Me-
mory andUnderAanding, is to draw s rude
Draoght of the Figure ot the Linda you ih-
teqd te meafure, not only as to the iides,
hat alfo the D agonals : Then meafure the
Lines upon the Ground correfpondent to
thofe on ths Paper, and fet the L'nei as you
meafuie them , upon the Sides of your
Draught, as if they were the true oni s, and
when you have finiOied yoiu Meafurin|,prc-
traa it truly, and it will do your BuAuefs.

Ijo Tf>e Tou/ig Surveyor*t Guide.

How to tek: the Plot of a Field from me Sta-
■ tion ttikin in the ,mUle thereof. bi tht
Chain.

. Fig- 91. L't ABCDE reprefenf theFidd
10 be plotted:, firft at K, I fet down a Stick,
then Meafore one Chain in L^rgth toward)
A, as K o, and alfo the L-'ogth of the whole
LineKA, which note down upon your rude
Dfai ght : N-Xt nifafurc one Chain in Length
towards B, ill K p, and alfo the L-ngth of
the t-ineKS; and n(?te it on your foul
Pra tight : Next you muft meafure the di-
fiance ber'A'iit o and p, and fo place it
iloivn upon your Drau^c.'

Andfol meafate one , Chain .in Length
towards C, as fi.g, agd .alftj the Length of
ihe.JL'be KCj ana' note it down upon
my. Hide Uraughr, as alto fhe diflaoce pg;
■And fo I proceed rpuiid the whole Field, '
and find them tp ht as. js^iotsd in the Fi-
gure following. ■/..,.

. iiw to PtotraB^ thhjt^t ': '_ .'

Firft (ake from 3'out Scale orie Chain in
L'-'ngth, thfn upon K as a Center, defcribe
the Circlenpq RS;neittatc from ytJul* Scale
2 Chains, tin L^ngthof ihtLine KA,and Htit
trnm K to A N xt fake^rom your Scale 172
Lin. and ittittrom o lil! it touch the Circle
irHi,and through -the point p, draw the
Line KB, making it to be in Xlengih 215 :

TJge Toang Survsyor^s' SuiJe- '■■' ^,131 .
Thentake from your Scale tbe Length of the ',
Line pq 13;, and fet it froip p to q, and '.
through ihe point q'draw^the Line KG,
making it to contain in Length 3i 6 : Nez4
rake from your Stale 112, itnd fet it from
q to R, and through tjic point R draw the
Line KD, and take from your' Scale jiy,
and fet it frpm K Co D i and &) proved till
you have finifhfd y bur Plot. I'^nd, Lafifyt
Threogh thefcytral .piQii)t#, A B G P, ftfc.
draw the. BQQndary Liocf' , - :

Haw to'tjkt iht Pht of. a FUU by the plam
TiibU^ at one tr more Stations.

. There afe three ways for doing this Work)
The firft. pexfortai tlje Work hj Mieafur-
ing every Line from tfia In{lril3ient to the
Angles, and is a good way, when it caa
be flpn^. The :fe(cond d&es -it^ by Meafur*
iiigpply the St^tioqsv Diflaoces, and is
VQfy qiick, , buf iiot (p fore and ^xa6t a^
the qtherj yet if it t« maoag'd hy ^
(kiifuU Aifift , it .will come near . ^oougfr ■
the matter in many Cafes { as Meafuring
for Mowing, pr Reaping Fields by-, the
Acre, or in Cafe ot Law Suits, whep yoq
cannot come nigh the Ground tobe.Mea-
fuired.

: The 3(? is by way ot Circiilatiijn, tVln-
flrument being oft to be planted, and tile plot
to be meafured by going roundabout if, by
which thick W90^s or Bogs amy bemeafared,
la

132 The Tmmg Surveyor* sGui^e.

\n alt thefe MethodB two things arc to
be performed.

1. At evei'y Angle whtre there is no
Mark already, as s Tree^ or £»/&, ftc. one
mud be pUced tfith s white Piper | or
otie muft go from Angle to Angle.

2. When ever yoa have occafion to plant
vour Innniment more then opcr, yoa muft
be ture to let it Itand jaft as it did the fitft
time, riiat is^'for S%ua1ion, which if your
Needle be giod, will perform the Work «
but is not itioughtfufiicient without a bad:-
fight and foce-iighr^ Now for the iiifi
Method,

To Uh the Btt of a Field at me Station; in
tny part thereof ^ from whence jou may fit
at itt AttiUs of Corneri.

■ Ff;. 92. Suppofe ABGDEF be a Field
to be meafured. Fitfl, Caufe marks to
he fet up in evei'y Cbruer of it i then
toake Ohoice of fooieconrement place there-
in, from Whence you may beft view all
the Angles thereof \ in which place at H
plant your. Table (covered with a Sheet of
tUott Paper J mm the Table about till (he
Nttile^ftand ovef the J'fciwr M Luee^
and fo faflen it with the Screw-pin, that
Ibe TibUffir nof^; Then placing your Index
upon the Table, lay the Fiducial Edge
thereof upon th? point H, reprefenting the
' place

The Toung Surveyor's Guide, igj
plare of youp Station-, and draw a Line
wuh yoor Coinpaffes point, b^ ihe fide of
the Index upon thr P^tpei ^ which done, dt>
re& your fight to B, (fiiU keepi}ig the Edge of
your Index to- the point H) and draw a Line
as before-, and fo in like manner direayouv
Index to C, D, E and F, drawirg the Linea
upon the Paper by the Edge of your Indei^
withthe point ot your Compafies, and fo
having finilhed theiatne, meaiiire w-iihyouf
Chain tbe^ftance of every of thof« Nfarks,
from the place ofyonr Station at H, and then
by the help of your Scale and GompalTw, Ctt
the fame diflances from the point H, in ihe
Ijines drawn upon the Table, making a
fmall ^ick with your CompaHes point ae
the end of ^ery one of l-bem ; then with
the point of your Black-lead PeniHl, draw
a fmall Line irom-poe point to another, as
namely from A to B, from fi to C, trom -
C to D, &c. fo (halt you hav» upon yMic
TibU'tbe' exaa P4ot of yaar Field.

To tjke the Hot of my Field at ofis Statm^
in any one Mile thereof^ from whence all o-
' iher j4^hi may he feen.

^'$■91 Firft,as before,fet upMaiks in ei ery
Corner of the Field, as at BCDEFG ^ ibm
make Choice afthe moft -convenient Angle
fhfrein ^ from whence 3rou m*y fcefl view ali
the refi, as A \ and having fizt-youi Table
there.

1^4 ^* Tamg Swvej/or's Guide.
there, 'as before ii raught , apply the ladez
to the point A, and direct the fights to B » -
then draw a Lne Afi upon the Taper, aod-
with your Chain meafurethe t-ength there*
of, and fet it down by the help of your
Scale from A to B.

Then from the faid point A, turn yout
fghta to C, your fecond Mark, ajid then
draw wiih onepciRt pf .youi Conip30fs up-
on the Paper theXine AC , mfafuring the
diftenee, and fetiing down the Lergh as
' you were before taught.

In like minner direft your Hghrs to D,
E, Fand G, and drawing Lines upon your
paper, meafure with your Chain the Di-
ftante of each of the fame f^oglts, from
your StatioB point aV A, where your Tab'e
H planted ? then with your CompafTes take
from the Scale the refpedi,ve diftances, and
vid fet them down from the point upon the
fevetal Lines, and fo defiribe the Lines
AB, BC, CD, D£, EF, FG,.GAi which
will Piaflly reprefent the juft F gure of
yoar Field. '■':.■

How to tah the Plot of a Field at two St<^i<mr,
when aU the J^glet cannot befeen at one.

It oftenttoies happei)eth, through Hills

ot the laigenefs qf Grounds, that you cm'

not from any one place of th- Field fee all

the Corners hereof j in wliifb Cafe you inufl

make

The Toung Surveyor's (hude» ' 1 5 j
make Choice of two convenient' places
within the fame ; Sa that here you are to
perform at two Srations^ what you did . be-
fore at one. '

T'g. SV4.S ippofd rVr'^for^j '^at the Figut^
CDEFGHiKLM, be a Fiel^l to be plotted j
I make Clioice of tw;o Stations, wittiin the
fame, as A and B» where I can. view all
the ADgles. Apd firft, I. plant my Tabic
at A, from whence , I can fee the A'-glei M
CD£Fi then plitcingi the jEdgpof iH7 In*
del lipon the point A, I ii.iuii my fight*
feverally to the Angles within my View, ai
to MCDEF, drawing Lines, rg is direflsd
in the F'gjirfli ]i((l)icli dpn?.,..I aieRfure
every pne of ^eca with) 01^ Qhain ,- and
n<4,i thdin ,doi|VA fr<>fn 'ny, Sp^Je^. -as
forjT^alyp i >! _j , _ ..■:, ;.'•■■ i

T.l)i^n (my Ta{>U' remaining' ^xt) t view (ha
other p^rts ot the Fie^d, and make choico
of (lie point B for.rqy feoijd . Station;
becaufe from rhehce, lean fee all .l)j? 0theis
AigIes,of the Fi^.i i^eo fettiijg up.aMirfc
thcie, I go b^ck tp:n3y firfl SutiiJO 9t A^.
(whiire mjTabhfivrds /«etf., «J lUfi it,) upott
which poini l move my Iiid<x, till ttirougli
t'le fights thereof, I efpy the M^rk atB, which
done, I draw a L'neby the Edge of (he fndej^
with the point of my Compafs,ei tending ic
the Length of ray Tabl«, as is reprcfeoied
by the Line ZXj which being thus per-
fcriaed, I meafure my Stationary diftance
AB.

n,,,.„..C(H)<;lc A

. -rvO^ Surveyor't Guide,
AB, 2 Chains which I fet off from \ to B,
(he place of my fecond Station, by the help
of my Scale and CompafTe!.

Stcmiljy I plant m; Table upon the point
B, and laying my Index upon the Line
ZX, I tarn the Table about, till through th«
fights I bshold my firft Statioir at A, then
I Screw the Tiri)le f aft to ihe fraff ; after-
wards moving my Indn 'Upon the point
B, I direfi the fights to- G, "drawing the ob-
fcureLine BG, containing i Chain 7?, then
sgain 1 dirt-d the Index to the Angle H,
«nd find it diftant from my Station i Chain
72 t and tlnis tnming my Index abont up-
on tbe point B, I draw' obfcure Lihes to the
other Angles as I did befbre, And meafbr-
ing tlieir refpeflive difian«> With-my. Chain.
I prick down the points I, K, L, npon my
Paper, ever obferving to lake off with my
Compafltis upon the Srale the exaft Quar- •
tity of -Chains and Links; meafured with
Cbe Chain.

: Lifffr, {The feveraJ pnttt9 or Anght »f tho
field, m CDEFGHIKLM^yeir^Jbtrnd oBt,
tad mark'd npm my fjper,) l' df aw the Boun-
dary Lines from point to point, which will
reprefent the -trae Plot.of tbe Field, to be
Meafiired.

To

X&tf TVttfig Svrvejters Guide, 137

To tah^he PJotofa Field r«mved from foUi
at 190 StJtiom^ when you are not pamit-
ted to comewitbht the fame.

^» 9T- If often happeneth that you are
.40 (rtesfiire a Field, and canno', either fer
W4ttrr Mooriih Grmjnd , or <)anger of
Suir, filter into it. S-ippofe the Field is
CDtFG, I iUflkeChoiceof (wo convcnint
Stations without ir, as A and B, from each
r>f which I can fee all the Ang'es of the
F.eld ; and having -planted my Table at A,
1 place the E'ilge ot my Index thereupon,
and direS toall the Angles of the Field're-
ipeSively, drawing Lines with the point of
my Compafles, as AG, AE, AF, AD, AC,
AH. Then my Table remaining fix'd, I
din^ the Index towards B, and having
drawn out my S'ationary Lme, I n^eafure
the diflanre thereof in the Field, and place
it on the Paper from A to B, then plant-
ing the TaMe at B, place your Index upon
the Stationary Line /B, and then move
the Table, till through ihe fight* you be-
hold yoor Station kt A ; which being ef-
fected, direct your Index-to alt the feveral
Angles of the Fi&'d, as you did before at
A ; and the interfedUons of thefe L'nes, will
give the points C, D, E, F, G, H, from
which draw the Lines CD, I>E, EF, FG,
GH, and HC, and you will have the true
Plot, and Frcpoifion of the Field. To '•

138 The Tottn£ Surveyor*! Guide,

To Survey Woai-lrnds bj the plain Table.

In very irrrgular Groundf wher« you
can make long Stations, you cannot fee all
the Anglfs from' each Station ; but in go-
ing 6a your Starionary Line, all the little
cornets in the Hedges may be feen -^ tbtref-
fore, that yoa may Plot all the Angles as
you mpafure on your Stationary Linct, ob«
ferve this G«neral Rule, vis.

A. General Rule.

In going on your Stationary Line, marfc
where an Angle (alls in aRight-Angle to your
Stationary Line, there plaiir the Table, lay-
ing your Indei upon the Stationary Line,
'■: and ttjrning your THb)e;H|)oh the Head of
J^our Staff, till yen can- fee either the Sta-
tion you came from, or that you are gor
ing to, (for Tov miifi ahap obfervi to neafure
in a fireight L»i^ from Station to Station, )
there fcrew it faft -, then obferve how fat
you have, mesfured on your Stationary
"Line, which diftanee take from your Scale,
and place trom yoor laft'Stationary I-ine,
there make a prick witli your Compaflei
point, and there take the Angl.p. ■

-IZiEw Toung Survejfir*! Gmde, \ 39

Example

K^. 96. Suppofing ABCDEFGHIKLM
N-^P, to be a greit Pool or Woo i : TI-QUgh
there be Fifteen' Aogles, I ptapt my Tible
only five timeg, vis. at :''EFH and M, and
upoD the dry Lines A£, FH, H M, and
M A, 1 raife their Perpendiculars in dpe
places, (according to M^i^fiin) and alfo of
a right heighih : By whicn and my five Sta-
tionary Angles, I draw the boundirgLines
qF the Plot, excluding, all the 7'^>a"g^'^s as
foreign to ir, they being no refemblancefl
^f any part of-the Pool, .but of Land ad*
2^ent. That if by reafonof troublefomS
9rulhTWood, Gorfe or Bogs, Cfc. I could
not have rneafured clofe to the fides EF,
Hi, or LM, it wwid be th« fame thing if
I went parallel to ihem. And this is a ihifl
that the P^a^ical 3<iveryors will oft be put
to make ufe o^

Now before I pais to rmthet Varieties let
iny Reader take oolice of thefe fcJIowing
things.,
. 1. That it is ihequickeft way to mearure,
fitft from the Inftrument to the firft Angle,
Slid then back froiji the fr-corid Angle to the
Inftrumenf, and la the reft in order 1, fiill
one from the Inftiument, and the other
to it.

2. In

140 Tht Toung Sarveyor'i Guide.

2. In all working by the plain Tible,
Tou mufl have a care that the Inftrumenj;
be Dot moved out of its due place, till
you have finiftied the work at the prefent
Station, for which purpofe call yonr Eye
now and then upon your NMdIe, obferving
whether ir hangs diredlly over the fame
pointy OB n-t it at whtnyou began your work,
and to rfflify your InRrument if ^aa fee
ciule. But becaufe all Inftrtimeprs have not
Keedles, inakeufe of the following help.

Whtn yoti have planted yonr Innrumenf,
and made a prkk on your Paper, repre-
feiiting your Station, fct the Edge of the
Index to itand turning it foftly abbut till you
find fome remarkable thing upon one fide of
ft^the Cloie, and another on the oppofite fide 2s
'••■' yflu look through the (fglw»ofypHrInder,an4
draw 3 remarkablfli'ne quite overyourPapert
then if you fufpea that by any accident thp
Inftruinem is removed, you may eafily trjr
and reftiFy it, bj applying the Indei to the
fame line, and making ofe of fore-fights and
bark-fights aE(»in , upon the fame marks
which you bel^bre oblerved upon the oppo-
fite fides Af the Clofe, And this i»a vJry
good way when you plant your Inftniinefot
lo the middle of the Fields ' ,

Ceiicenrhfg

The Tomg Surveyor's Gwd»> .14^

Covcnmvf, ibe Phttirg of mttty Chfes tf^ftber,
wbet^tbe Ground he even orwieven. .

^S 97Sstfppofe.ABCDEFGHlKLM to .
be a Tenement or fmall Detnefii dtvitled
into 14 Clofes, to be meafur^d and prc-
trafled according to their fevtral fhapes
apd Stituation. I firft draw the Plot
of the whole by the method of CircuIatioHi
this being done, a Line from A to C gives
the Triangular Clofe ABC, for the firft.
In the next place, tgo round the (wo Clofes
■ beginning at A, then at C, and fn about
to A again : And then for the third Clofe,
I plant my Table at p, and go round to C,
rhe line CD being prorraded' akeady, an^
fo of all the reft, flillobfetvirg which are
comnioB iiries belonging to feueral CloJes,
that yh\i may avoi3 the meafuring of lims
iHore than oncp, and l^y every parr of every
Clofe in its du? place; that you befiire (o
keep (he Inftru^ent. throughout the whole
work to its true pofitioiiby Keedle, fore-
^ght 'ind back fight.

Theri' are I confefs divers other ways of
doing this work, but none more fare. .

2. If you are to makeaMapofaLordfhip,
.walk over the Lordlhip '2 or 3 rimes, nl!
you can bear the Map of it in your Head,
that you may the better conceive to carry
on the whole work, and to make choice o€
the

142 The Toung Surveyor*s Guide*
the fitteft ]tlace for your Stations. Plot your
Townfhip firfl:, beginning in the mnrt con-
venient place to maki; your fitff Station as
long as pofllble.youcan ; and Jik^wife from
your main Stations, taking therefrom all
Oat-Houfes, and little intermediate Officfs,
and then return to your meaa Station a-
gain.

Ohftriti thit Gtneral SmU.

When you cannot perform from your
main Station, or fee all the Angles, or Back-
fides near joinirg thereupon, to make inner
Stations as before, and to perform the vTorfc
of each main Station with inner Stations,
till the TpwnOiip be finilhed.

And where you conclude your Town-
fhip fromTour iaft main Station, direft your
fights to a Station in fome convenient place
of the adjoining Fields j fo may you take
the Plot thereof from as many Stations as
need requlTes, fo will fuch Grounds be join-
ed to the To'wnlhip, and fo may yoa pro-
ceed with next adjoining Giounds.

Your Townfhip being by the preccdii^
Rtiks cwnpleated upon your Table, with
as many of the adjoining Grounds as will
come thereupon, make Marks upon your
Plot as you proceed with yoar Work,
where the next Ground joins or falls upoii
tfaofe Fences you have already plotted.

The Toung Surveyor's (juide, 14;
that you may Jcnow, wheayoi^ve raken
the Plot of the feverab Fields joining up.
on your former Plot, how to join them
therete.

Proceed where you left ofF, and take as
many of the Incl'oftires upon your Table at
it will bear, and join them to the foimer
work, by the diredions of the Marks befon-*
mentioned ; and in this order proceed till
the whole Lordlhip be fioiftied, obferving
to. dtfcribe upon your Plot all Roads, and
whatever is remarkable that you me't with
in your way. Obferve to place the Trees,
in. each Htdge>Tnw, fo that the Landlord
or Owner (hereof may know by infpeding
<he M»p what Fences belong to eaih
^Gtonod.

The trve metboi of takh^ the Plot of Toteven
Hi9y Grounds, in rfJpfS of their trm ^um-
tity^ by the plain Table.

I. InGrounds wtore tbare are multiplicity
of Hills' running oat: into apother Irregu-
iarly , place Betcbni upon ferveral 'oF
the Hei^ft ot the mnft nwterial Hills,
whether you can ffe the Angles in the
Hedges, or (he Hedges themlelvra from
ldv«ralofthe filid Hills, and direfl yoar
^hts from Station to Sraticoi, laying down
each Stationary diftance upon your Paper
with your Scula , placing :yam Sratjon'
Marks

144 "^ Toiing Survejfor^s GuuU,
Marks fo, that ytmr Ch in in mfafating
(hefe Stationary diftancts may pafs over
(he mo/l materiil HiUs in the Giouad, as
we fhall here demonflrate;
■ 2. fV^.sd.Admitthe Figure noted with AB
CDEF, f^c be a Hilly Ground to be. plot-
ted, whof: jsft number ot Arrfs is rtg'iired;
fi;t up Heacons or . Stationary Marks apon
the (Op of moft ot ihe nalecial Hilla, as X,
W J, 6 y, z, *,

3. plant yrcr Tafele at X, your 'fitft
Station, direding yoilr fights therefrom,- 1*
the Angle Di then with your Chain mea-.
fure the diftance X D on the Ground, vrhich
take from your Scale and fet trom X to D,
where make a'priclc ; tb^n direQ your fighti
Co E, which diflance take from your Scale
and fet from X to E ^ then direfl; your fights
to F,- Whiph "prick off ffom X to F on the
Papft } then again direa your fights to G
and H, and mfafure the Ground Xjne8,urhich
ftt off upiJH your Paper ? fo have you
finlflierf (he work trf your firft Station. ■

4^ 'DxfSi'ihefote yov alter the Table i at k
fiords planted at the fi>fi Station) your, fights
to your feccoid Station at W, driwing yoai
Stationary Line by (he Edge of your Jndezj
and mekfure the Letigh of the faid S atio-
nary Line on the Ground, which take from
your :S^al% and fet from X to W, where
place down yotir Table, laying the Edge
of your Index apoa the SratioQwy Line
XWj

The Tbung Surveyor's Guide* 145
aCWi yoDriodfxri-ft ng in this poftiirei^ turn
*he Tsble gentty-qpon thetkad of" your three
JLegEetl Staff, till through theifightsyoa
fee ttie lirftSiation iraijcat X, where fcrew
itfafti then direftyDnr fights to all your
ftreral Angles in view, is K,-L,M, and mea-
tiire their feveral diftances trom your Sta-
tion at W, . wfeich feveral diftances lake
ftODi puf Scak:and prirk off upon iheir
Rcrpe^pe Lines, ppan your Papen. :

-y. '. Theri" (to b'efote) dirtft your fights
to 9 ycui Third Station, and draw a
Line by ihe Edge of you. Index, thej,
meafure on the Ground from W to cf
which take from your Scald' and fet-pnyout
Paper from W to J, where plant yoae
T^le, as ! wai before directed, at your laft
Station; '

Now, becaure you nmnot fee your Fencffl
in any part of the Ground by reafon of
itie Hill fi-otn this Station, therefore di'rea
your fg^ts to b , ymir fourth Star jon,which
diftance S ft, nieaftre on the -Ground, which
take from your Scale, and fet from ^ to
.*r, wherfr-plant your Table by the former
dire£lions, nd drrea your fights to y, yout
fifth Sration; then meafure the the Sation-
ary diftmce h y, which take from yoar
Scale , and : place from h to y, wherft
plant yoor T^Ie.

■ 6. Then direft yotrr fights from your

-SiatioQ at y, and therefrom ob(erv«, mea-

H fufe

^6 The Toung Snrvey^r^s Guide.
ire, and \*y dourn apon yoar Paper, ai
ou were directed ar your other Statiofli %
Mn dire^ ynur fights to your fiidi&'aiioii
'. z, and ftfike a Lineby the Edgt^ yoar
idez for your 5 ationary Line, wTiich tak«
oin youi Scale, aad fet from y tosVivliere
lant niir Tabic by the /tiregoing dirf£ltonF.

7. . Vout Table being (planted -M z; direct
our fights to all the Angle* ia vkw, and
rike Lines by the Ed^e of your Uidu
ier«to, astoO; P, Q, R,fi,T, asd c?ca-
ire tbeir diftances on (he Ground from your
lacxof Aanding; which fcveral diftances
ike from youi: Srale, and fet itoen Z, to
>, P, Q, R, S, T,- whtre make pricks with
oar Compaifes point \ whith doae dire^
our ^ghts to ynit Tti, or laft Station*
rawing a Line by ih« Edge of your Ind^x
>r ih« I^Srationary Line; then meafure
e diftanoe Z * % which take from your
ale, and f«^t from Zto *, (aa before uuglt)
here plant your Tnhle i which done, di-
a ycur fights to the Angle N, which di-
nee raearurc on, the Gtourd, and then
CB from your Sc&le and fet from * to
where make a prick ; fo hav« you prickl
' all the A^gles in the Field,

8. Lajily., From the feveral pritks, as rr-ini
to B, from B to C, and fo to D, (^c-
w Liies tliei'efrom till yoti come again
A , which fltall include the Motmtaioaus
Id : which was required.

And

The Tou^ Sttfveyor^s Guide. 147
And here you n^ay obferve,that the Chain
1>eing drawn over all the Hills and Dales,
muft necefTarily produce a larger Plot, vis,
more Ground, then giing round abcut the
Hedges all the way upon Ivvel or even
Cronnd ro plot (he fame : Hence I may
affirm,that ihisjway ought to be pradifed by
&irveyors j from which ^ap the true Nun>
ber or ?cm is found tfiat Jhe faid Ground
contaiileth.

CMcmihis Shiftily of Paper^

U vtty ordinarily fella out in praflrcev
■wiTh your Table, as it is covered wiihPaper,
is too little in feveral Cafes, e^cially in
gceaf. Grounds ; in fuch CaOs when yoa
nave proceeded as tar as you can, till the
Lines tun off your Table or Paper, you
muH ibi't your Paper, and put a fair fheet
upon the Table.

, Firfi then, upon your laft Stationary Line
which runs off yoar Table, obferve to
fliift that Sheet fo far off or befide the T^*
ble,that yoor laft Sution marked thereupon,
may be ma(k<:d jtiftupon the Table to u^hi'^h
Sheet in this order glew a fair S'lset with .
Mouth Glew, and fo faAenthem down with
the Frame of the Table.

Second; hay a Ruler upon that part of the

Stationary Line^ from the Station, which as

t faid beioce. ii juil upon the Edge at the

H a Table.

■I.4S . The Toung Surveyor'' sXju'uHe.
Tablf, and draw or augment thiit Line oh
the fair Paper, upon whith Line prick off
yQiirSiationary difiancc

Tbhd^ Upon this Stationary Line I37
-lite Edge ot your Index, then tot n the
Table upon the Head of your S'aff, tiH
(hrough the fights you W the iaft Station
,yriu direded-ioi lo will yJiir Table be
jTydlified to proceed with your work.

£xatriple_

Fig. 99. Admit the following Fig'!re G H
JKLMN OPQtRSTU WX, reprefent
a Field to be plotted by the plain Table, '
fwhich is To ]ai,ge that it cannot all be plotted
«n the Table ^ and becaufe I would - nave as
much upon theXableas it will bear, 1 be-
gin 39 una the tt'.ge of my Table as I can }
let us fuppofe (lie Tatjle witfitn the
Frame to be underftood by ^ the Line
•YA, therefore J make choice to begin at A,
planting my Table there, and direSing my
■Jiijhts to F i J mcafure the Stationaty d;-
^ance /^f, which is almofi: the Length
of the Table ; then I come bade to my fiift
Swtion, and tliere again pbnt my T^ble in
-fhe fame poflure I did at fifft, fo diredfcing
the fights to B, taking (he Angles by the
,«wa>', then to direi^ my fights to C, where
*J plant my Table, taking myAiigks there-'
Irotn ihat are in view .j next I direft the fights

li«*>--l

The Toung Surveyor's Guide: 149-.
to the Station at D, drawing.a Line by ihe
Edge of the Index to the farther end of ihe-
Table,as Cd, where- it runs off ihe Tablej,
then becaiif^ I can proceed' no firther before
1" fliift my Pipfr, and put a tlean Iheet up-
on the Table ; I take this (heet off, and witfii
Mouth Glew, I glew another fheet to, it at
TY ; then I put thsrn both together upon-
(he Table in this order^ viz. I bring the
Station C, to the S.'ationB, upon the Table^,
and fo fallen them down with the Frame^
To that the line zz,. poffefTeth the place of
the Line AB^ fo that part of the Plot iS'
yet upon the Table, vis.. from-C to e, and
. the reft of the Table being covered withfair
Paper j^then plant again your Table at the
S;ation C,, laj'ing the Edge of the Index,
upon that part of the Sranonary Line, which-
was drawn before your Pjp;f was fliifted,
tf/z. C e, and extend it to D, upon your
fair Paper, and then proceed to finiihyouc-
Plof.

Note, There is another way to- perfnnn-
this work, viz. !y the Scales-of equal parts;
upon the Frame of the Table, whicii is
taught in feveral Authors.

*'50 The Tetmg Surveyor*! GuiJe*.

Xo taie the Plot of my Cbamphit FuJd -zcattaitt-.
hig 20Q0, or 5000, Acres of Grotiftd, by the
plain Tdble^ and jet never hejirced to cbangt
' jour Faper,

Too muftinthisCare place youfl'nfTroment
ift eveiyAogle, and fo get everj- Arg1e;antl
i(s Sdrs, not regarding the Length of ihe,
containing Sides, as you ufe to do, then
muft you msafure every Hedg, and as.
yon were wont to lay the fame down
by your Scale and Compafles. Here you.
ihall only write the Length of erery Hedge
upon the Line? drawn upan your Paper,
and correfponding ihereunto, fo have yon fi-
nifttd*, and you ffiall never be forced to (hi ft
your Paper, nor have the L'nes to run ofF
the fame ,' for you may draw them as
]bng, or as fhort as you pteafe. i4iw when.
y.>u come home, Upon lome ftieetof Paper,
prdtraft all the Angles one after another; as
y.iu found themtn the Field, altowirg fcy
your Scale andCompaffes every Line its due
Length : According as y.iu find the fame,
note thefcFigurcs upon the faid correfpondent
Lines, and you will produce a Figure like,
and Proportional to the Field propofed.
^\)\i is moft excellent for large Champion
(^oupds,. and therefore worthy of Note.

Bom.

The Towig Surveyor*! GniJe, 1 51

fiow to .hiom vhether a Flot be truly taken, by
pi oviyi$ the work tit every Station ; a«i in
caft of Errors how to fnd and CorreS them^
before you are too- far yafi them ^ by tbt
plain Tahie.

• Firft^ In -tfie i^Ottii^ any Field by the

Slain Table; beliKC to; lot your Statioa
Urics ftand »p in eteiy hole till you
have finiflied your. Ploi 9 and likewife
Marks in raottof the nraterial Angle»
of the'FiftWi .«bkh J!7 rhe following
diteaons will inform you whether yoo
tatE-dbtwr-ght'or-iiot; andin CiTiot an
Errw cbinniiii«d,,;howi.toiind wlwre it if.
! iStcfflfJ; WtewyoHarBdaparttdfromyout
£rft Sration, nid- (five prceeedrd to yoMt
UxxtnA, and taken all your Angl« by
the.wa/, and* planted your Table ac
yaoi'^ond Sfxt^im, in- ordei to proceid to

Sour third S^atiisi , .arid would kiacw wbe<
lei iRe work of yoiff^ifl and', fecorid S*a- •
tion be' right or imi : Direft your rg'^is.
to one oi moreof the mofi m'sterial An^tles
fton iotk, tK.yeu pnoc^dcd frcm your f\ (I
«o yonc.ftcond; Staflioi); znA if- taeEdge-
bf jDUBlndfaEtHt the Anglesupon thr Pinr,
jTMi worJiiis'^fo: far tialTr taken, :otherwi£j
not. 'i'" ■

Tbhii When you hawplantedyoinTible-

at yoor liucd ir'ation, and t-dkea all the

H. 4^ ADgle»

i$2 The Toung Siirveyor^s Guide*
Angle* \,y the wayj then dirffl your fight»
10 your firft Station i and i* you find (he
Edge of your Indeifo cut your firft Station
upon your Plor, youi wrak isfiaflly per-
forraed to your third. Station, where you
then are : But in csfe you cannot fee your
fifft -Station mark from your third Station,
er place of fianding, thnD according to the
hft Rale of direflions, diren; yaur. fighli ti^
fome Angle in tiie Field whidi you< have
taken upon your Blot, -and if the: Edge
of youf Indei, cut the fane Angle upon
your Pbt, yonr orosk is righc^ otheicwife

BOt; . ,

P(mthXiktvrKe.v/)nn yonj Table isright^
\j placed or planted .at'yoar fourth Statlp
on, and all the Angles betwixt your third
and founh Stajion, beir^ taken, ca& youz
Eye into fbat pact of ctie: Field . yon have
plotted' I and vie#~ which of yotjr Station
Marks ~yoiB.caa fee( t\\ss you ftre already
tome Fcoait. toi£i..'.eiihar firn orfd«ind} aa
fuppofe you'could fee only :your feccno ^
S'aiion mark, then dire^ your £ghts from
your fourth Station, or place of Handing;
to yooF- ftcond Station s, and: if dre Edge
of the Index ; cut the fecond . Sfatioa upoo
the Plor, your work it iaiat performed
right,. otherwi£:' not ; and if at any tiinc
you cannot fee fome one or more of your
Beacona oriBtationBCjr marks, befides the lafl
you can« fiom,ihat yon have already pa jTed^

. ■. then.

The Toung Survejcr's Gtiide. 1 5§
tflf n nuke afe ot fome AngIe,to prove your
Plot hy^ as I fsid before j and by obferv-
ing this Method, 'tiseafie to know whether
yon have committed any Error or nor, and
a you have, how and fpeedily to find'it
before you be gone far pafl it^ which is fo-
plain and eafie , . that it need* no farther^
Demonflration.

The }>ej{ vay ofMijJinit^ the fever ^l, avi par-
thttUr ^atttites of Arrable-Lmis ^ ^^ty
and Meadovs , ^ivg-w the open or comaiia'
Fielii!, vitbp'ott DheSiom for the taidv^
in and inclofittg a hordjhif.

When the Sarvcyor i» to proceed abnufc
the Survey ot a Lordlhip, or Mannor,
wheretn the Lord 4nd Freeholders are z~
greed to improve it, in laying each Mans^
Land together 1 it will be convenient to-
begin at one fide ef the Field, and there
fet down the name of your 6rfl Furlong ^
IB a Etook of a> Qiiue of Paper, where-
in each .Page is ~ divided into fix.
Columns, fo as the two firfl towards the
X-eft-hand fhall ferve the Breadth of the-
Band at each end; the third or greater "
Column, Iliall ontain the number ofeveiytr
Msna Lands, and alfo his Name ; and the
4tb, 5fA, and 6tb, for the reduced Lengthy
Breadth, and Qtjantify<^

i^J4 7fo Tdung Skrwfcr^ Guu&,

Neit afrer you have thus done, andare
coaif to ihe Fmlong where you began, «-
prefs in yMt Boolcthe Nitne of jrourEidd,
and ihe Furlong ; then in the middlemen,
or greater Column, note down tbe Kama
of the Free-holder that firft begins if, with
the number of hit Landi^ againft which in
(he two firtl Columos towards the I.eft4iand,
wricc the Breadth of the Lands at each end^.
nnd in the three laA put the redaced
breadth. Length and Q.u3ntity; which
done, fttt down the Hjme of the Free-holder
that liei neit, and the number of his LamfSj
together wirh the Length, Bteadth and q'jan-.
(iiy, as before, and fo proceed in order
till fou have finifhed the Fiirlong.

And To on from one Furlong to anor
ther, till you have finiflied the wbola-
field. -■- ,

But that you may the more fbll^'jiadex,-'
ftand the Form thereof.- I ftiall' Dieur jrtm
iin (be following Example an sb^o-
hire Method ,. how you may rffefl th»

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. Cin><;l.-

After ihi< manner you are to praceed

ffom one f iirloog to another, until yott-
have finifhfd your Field-Book ; whicb,be-
ing done, you are next to make a particu-
lar ^f> -every Mans ,ArraUe,'iLeys. ai>d, Alfa-
dows feveiaUy,: to wh^kh pufpofc,' upon a
&ir {hee^of Paper, y&uafe to make fa
many Columns , as there are Free~-
holders , every one whereof ia -to 5e
rufadivided iattt liine, .Ib'wil] the.firftferve
feit, Arnhtei ^di& feeand' :;for Ley! Ground,
afid ihi third andr UR foe Meadow, if
di^re be "any t And if oneftieet -will not
contain the whole, 'then may you-tjike two-
Off. three,' or fo 'mani^ as you Set coi>
nribieBt..''- ■ .- . '

.Nets ym^.-3i«tii take the PIot,'i«ld~ gr>.
Beralfiurfie}'' oi'.the whale, accordit^to tha-
RaJBf'. be'bre dF^ireretd, land fe^ if t^e Suifi
rtf-aDlh^'Edttfcalaffe agree with the Totai,
t&en ydu.may couelade the work is^Ngbr,
bnhf ^oft-conuoonly the I^rticubrs willi
faine#httte2!ce(d the IBeueral Survey^' and)
i^-:'diis.'.6are,' t^at: both 'may agree, you-
arbtibiiredtiratlie Satmitf i-veiy Mastf ?ai- .
tfliubrt anfttKKabte to-'the'-Proportionbf his^^
QoDund, whkh may b tfiefied by the Gol-
den Rule. Far, if in the whole Eield
fi^nciurdinit it be- loou Jcrtr/tht Particulars^
exo'eed iNe: Ofeuerai. Sferwey g'Acrefl,! .whut
B\3ii]:^oiJic^ei}'liit,ji^Jh'nivfHi\be, 8 Psrofans,-
aod & il»i(:ti£:.asf lo detlna out-ot theSum^

15^ T£* T^ung Si»v^f^f<^itfy*
Totflt of flich a Msn» PafttcnlBn^ acoofding
to which lam to Plot him t^AcKs jRouIf,.
32 Percbce. And fi> of the* reft.

Bo9 to tale tht Phti>f'd J^Hfr'oih- me 9i*-
tStm tahlH ht the mSdU tiKivrf, hj. the'
TbeodbSte-y or kf the Bigre^t on-- tb»
glaht Tahie. <.

%. locLet ABCDm n^^nt the Ftgn^
of sField tabr pIbttedbytfaeplaioTdble'
in Rainy W«aihet. - putod thd £rabM--:
wilhdor a Paf^r,: .tbc gridutcd. liile.^p-'
wards, and plant it in fame ranvcnieiU'
place, whence 1 ran k* all t^e AngJes, as.
at Qy then Blaring the Index upcn ^tJ.
Tablei^tbatitie^fidudal Edacckitb tf' ifw
(acae'tinw time <go ihtougfit tba Center vp^'.
on .the 'Bible, and tfae.linnitrpoiithfrFmitvt-
of the Table cutting it Peipoodichlatty at
^^Qy (.vbert tht Dorset b.^gm and. end) and
i,^o(tbsax»B £r<i/^^ Ifnrn aboDtthe TaMe
upon the &aff heady till thiiotigh the 'Hf^YA^
(tbefde vt«rkei:with iSa btiiif^ neah-iUhte. E^e^-
tfee the Angk A, and theirs £.-i*Br^itfeft;
obferving, where tay Needle eotteth, I'^nd'-
by harlcfight-oaufinga-Maik tatefetuffcin-
tlle Bine CD at ihc point E, tliat the in^.
finimenftnvy beJupc iirni tI»mv^mobntg^
\,or. h r^ftdif , a k notKj^Xdunrg-thcd
Work ''A|ld.d<MVJhe'l^ibe^Of^p8i^liIlgltp^:

UOdcB

The Toung Saneyor^s Gutt^ t Jgc
under . the fights of ^« InflnitxKRt to the
mark at F, is ("j it were) the^prime Dis-
meter whence the D gree&of the Arglea are
to be numbred, and accordingly 1 matk;
the Aagie A^ in my Tai>k hereafter to
beeiemplified with ^£o Degree*^ But tq
proceed, tmnang' the Index with tht fi-
ducial Edge Dpon the, Center, til) J £ee
that Thread ratiitig the Mark at at B,
the &id Edge cats upon the Frame at 76
Degrees t; Minoitesr 1 note downfdt thai.
Angle : Tile like work I do, tm-ning (he-
ights to C,E1 and. E, (but not to F, for thert
it no jitigle but only a Mark in the Bouniatyy.
and i find mine Index, to cut for, every An-
gle as Ihave Marked the[n,withiB the prick-
ed Circle of the laft Figure, w». 157 deg..
«. Miootes for C, ' 225 degrees 20 Minute*.
ipr D, and 27% Degrees aad 5P Minutes
fiw E.

Then I meaftffe (w cmfftohpilthf mM--
SueJ.: bf othirt) the di&ancei-
Tirtwixt the place where ;the _3^ ''""''
biflruinent flbads; and ev» |_L?_I
igr Angle, and fiid them to A|3io|
lobeasIbiKretthftnupai'^ 1^^;
the pricked Linei in the little ( dII,^ !o
QkIc, mV a 4. Chaiui 20 [eU?*! ,
- li^nks, B 4 Chains 3 Ijyiks, I

C 3 Chains 8^ L^nks, D 5. Chains 35; Links,
C ^ Chains 6 Links. And now my Table
hotlL for Lines and Angles is ihiu perfedl--

iitfo The Tmmg Surveyor*t GmJe^
ed, and the work is ready foe Protra^ioD
irirhin DoorF.

Now to protrad our Obfervatioix : Idrav
upon Paper a Line A F at rtdventurr,
fi> it be long enot^h, and (lick a [nn in it
at pleafure tor the Center O, upon which
I' place th« Center of the Pro(ra<5):r>r,. (a_
that -the fireighr fide of the Crolrador majp
lye upon the Line AF*, the Limb or Arch*
edfide being upwards towards B^ hy the
help whtreoF I make b prick on the Paper at
•^tf dfg. 15 Mill JorB, and at i;7deg. 55^
Min. tor c, accoiding to.the nambm in my
Fie)d-Book.

Then turnitig the Ptorra&or aboat. the
pin, with the Litnb down towards, I) and E„
till theDiameter 1/c again juftnpen-the Line
AF, I nambef downwards (rom the Right-

' hand' towards (he Left, beginning 190, 200,
€5*^. And ove-ragainft the place where 225:
digrees 20 Minutes and 278 degrees yo
Mintires fall, I prick the Paper at the £de
q\ the L'lrtb, and thfoagh thofe fow
poinW. I.draw i^a mJny feveral Lines^; up--
onwhich,an!l alfoiipon tfieL'.ne A O, Iimrk^
out by points the- (rue nieaiiMe of nVAty Licet
fa^a Scaleitroni theCenrer, ami from thofe-
point§ drawing the £ines AB» EC, CL), DE^

ud ££j I have the tuie Piotof tlie Fipid.

The Totmg Surveyors Guide, tSt

H't" to Jiihe the plot of an, hrsguUr FieU hjr
the TTjeodoUte or liy the Dtgrees cti the plaiu
Tabkbygoir^touvd the fame ^ being the beji
M tbod hi PraSice.

i"^. loi Firft caufe marks- to b« ftt up at
every Station, » A, B, C. D, E, F i tVa
inalcing Choice of a Station at A to begin
at:' Meffure from A; to th« Hedge at
a, which you'll Cnd.to.be ^5 Linksi wl^ich-
Dote down in your Eye draught cr Field
Book y likewife mcafHre from A, to tho
Hedge at b,|ind you'll fipd it to be 20 Links^ .
whioi Note down i then meafureirom yout
S'^atipn At. towards B yoar fecond Staiioir.
.ftP^ ^ f c- ;4P ^ .■yow have an oS-f«t of
jo.Li'nkatoi the right at the corner c, and
- at Sc.^aKyoa have meafuced to your fecond
Station Bf B) where you are to fix your In*
firi^nent 9nd take^the Argle AB'J, which
V-fo^r^ ta;be 12^° jo.' which note down-^
^p meaiure from your Station -B to yoor
StationC: i^hich contains. ;c. 2j/.atSt^ioH
C, meafure to the Hedge at right Angles to
di whichletbe-35Linki,and fromC to the
Hedge at e , is zo Links , fixity yoos
loftlttHKlU at C take the Angle : BCD,
which cppiaitisj 104* q'} then meafure is a
ftreight Line from C : tawardft D, ainl at i c,
70 /. you have an off-fet to the Ccnrner at f,
which contains 3; Links; at 2c. ;of.you
bare an b0'-(et to the Corocr; g : which is

1 6i The Toung Surwyor^s Guidf,

I f. 20 /. at 3 c. poil you have another, at )h
of I c 40 JL then oieafuring on 6 c, 30 J. yoi
are come to yooF Station Di mature from
D to the Hedge at right ArgUs to i,
whichia 80 Links, and from D to k : whicb
ii 50 Linkii Th«i fiivfiur InllnimeBt at
D: andiakethe Angle CDEi whichisy?*
30' : Meafurmg along tfie lM\i DE, vooll
find that at 3 c. 60I. yeu have anolf fet of
1 c. 50 1. to the Angle at Ir and at 8 ?. j"57.
yon have an cfF-fet of i c. 50/. to^he Arglt-
at m : asi at 1 3 c. 20 !■ you ha^e meafured
10 yourStationat E: froni E to the Het^e
»» T^t Angln meafiire t& n : which ii ;d
L'nks.and fromEto 6, wM<his ^o tinfts at- '
fo: Thmfii your rnftrumenf-fifiatE,.and
take the'Angie DEF, ■ vi'hich i* f9' ^: b\
then meaGiringina iRrfight line fioniE to-
wirds F: you'll find that at 4 c .• jo t yoa
. tonch the H*dg«, and at 8 c; 3c»-I. yon liave
incdfured to yonr Station at F; Fffiih F
Mtbe Corner q, ■ Wright Angles conraibi
53XinkSi--b#cawfi: you have meafiireJ'^to
the very Corned, you have no occafTon M
meafiire from the Sratitm F , to the Hedge
af.r; Having fiit -yoot Irifirumerit at F r
lalte the Angle-E FA whichcdntafms *q 8"
St/ then me^furing'frdm Fr tpwilds A
yda'll i]nd<rhat at -2 c, '70 /. you ha4t an off-
fet of 8y L=nk»rffrh'e'bend af S:' rfiMl rt
6tf. 65 J -yen have mealwred to -youf firft
Sration at A ; wJBie yeu began.

Jhe Toun^ Surveyor's Gaidt. itf j

Nov toprotra3 tbeje Ohfervatiaii:..

Firfi draw an obfcure line at pUafure, at
AB,then with your thiDB.aIer,having 27f qual
parrtinanlnch plaeed upon the very Edge
(hfitig tht Kumher that this Brav^ht ip/w yro-
traSid by) appFy the Edge 6f this Ruler
to the L'ne ' AB, and with your protraffc-
ing pin make a mark at 3; Links, from A
lo a; then place tfic Edge of your Ruler at
tight Angles to the line AB, and prick oft
so Links from A to b : then phce the be-'
ginning of your Scale at the point A : tfii
Edge l«ing laid alorg the Line AB, by
your Field Book or Eye Draoght you'll find
rfcat at 6 c. 40 f. you hai'e an off-fit to the
Corner c: which accordingly prick ofF, and-
drivr-lbe Black-line be, then at 6c. "jot
prick off the length of the Line AB; at the
point B,- with your protraanr lay down
•he quantity of the ArgTe ABC 126"^ : ?'b,
^nd with Toar thin Ruler prick off upoii
the Line BC 3 c. 35 from B to C, at the
Statioil C: prick off 25 Links to d, and 20
' Unks to c : both being at right Angles ^at
Ihe point C : Piotia^ the qiiaittity oP the
Angle BCD 104' o', then with yonr Scale
firiik off npon the Ime CD I c.yol and at
r'ght Angles to thfs point prick off 25,
Links to the Hedge at f : Then draw year
boundary Line throagh the point f and e.*

1^4 ^^ Toung Surveyor's Gaide^
And likewire ihrnugh c, and d, and where-
thefe Lines Interfe^ giiret, you. the very
corner ar j : Next from the point C, priclc
off 2 c.%Ci I. and at right Anglei to the point
at 2 c. jo/, prick off i c. 20 /. to the Hed^
at g, and draw the black Line g f : N«xt
from the point C : prick off 3 c. 9a /. and
at that diflance prick off* i c 40 f at right
Argues, to the Hedge at h, and dratv the.
Black-line h g,then tram the point C prick of£
& c. 30 /. to die Station at D j at this S-a-.
tion D prick off So Links to- the H^dge at
c, and ;o Links to k, both at right Anglesc
At the Station D prick the Qiiantity of the
Angle CDE with ypur protractor, whirfc
(ontains n%' 30' then from the point D,
Viih yotir Scale prick cfF ^c. 60I. and at
r'^ht Angles to this Mark lad fet off, prick.
oti I c ^° It to the Angle at C, and draw
the Lines Ik and h i, till the; inteiffO.
each other, which will give^ou rfie corner
(itz.,At the Station.D, Pnckoff^Sc. 15,/^-
from yout Scale of tqual p9ri8,and at right
Angles to this laft Mark prick off i c. 50 /.
to the Angle at m; and draw the Black-
line m I. Ar the Station D, prick, off' upon
the Line DE 1 3,f. 20 I. to the Station at Ej
fromthis S.atron priib off jo Jj^riks at
eight A^gka tp.the Hedge at n^acd 30 Lin.
to-.the Hedgft at 05 at the, point E protraft
the Quantify of ,(he Angle DEE with your
grotrai^or , which contains $i9>' '. o''ihen
. ' ' * fronk.

The Toung Swveyor's Guide. 1S5
frf4n the point E prick off 4c 10 /. where
at louchfs the Hedge at p, then prick off
&€. 30 /. to your Station at F. prick off ai
the point F yo L'nks at right Ang'es to
the corner at g, ihen draw the Blatk-Jines
pq po. Likewiiedraw the Biack-iincs m n-
where (he two X^ines m n and p o Interfeft
^ives -you the very cotner of the Field at
y: at the point F, prottafit the Quantity of
the /Ingle EFA with your protraftor, which
contains loS" 3kj, and if the Line FA falls
in (he point A-, year work is rfg'it fo far:
From the point F prick off 2 c. 70 /. from
which pcanr prick off at r%tit Angles 85
■Links 'o the Atigle at s ; then from the
^oini F priik off 6 c. 6')t. and if 6 c. 6^1,
tench s jbfl to the poiTj' A,ycu msy be aflu:-
ed your Survey was taken truly, To enclofe
your Field draw the Blaik-line from q to
8. and from b to a, the line c b and f a be-
ing contintifd, will intefftct at w, the very
corner which enclofea your Field,

N. B. As I have reroniinended io ihii
iiiample the thin Ruler with t-qual 'partj,
upon iJie very Edge to protrfia with , be*
ing mjjch better than Compaffes on
many Accounts, as every fi-jrveyor will
' find. So I wouM adwfe every S'lrvpyor,
that is curious, to make ufe of Mr If^jrdi
Proiraftor improved : The Semi-Circle is
inade near as ufual jupon thij Semi-Circle ii
jnoveabl* Index of 7 Inches lorg,theuppec
put

iS<5 The Tbung Surveyor's Gm3e* ■
part bfing ; degrees from the Center, and-
the lower psrt next the Limb } 4 Degrees, fb
that pach E<4ge wit] be Diagnnal of ooe deg.
\-tipoa this. Edge '^ unequal Pivifioos Caicu-
) laced to every Minnie. This DefcriptioD is
''' -accordirg to Mr Warir^ inftead ot having
the Index thiis made, I think it much better
>to have that part of the Index above the
tAcnb to be part of aa Arch of two degrees,
and th« other part fu^pofed to pafs thro'
th^Centre:Now upon this Index thfDIvifiant
will be fqual, and will be conliderably -
larger at the beginning of the DiviHons ihaa
ID the other. The D^oionflration oT this de>-
pends uponTfco. 1 3 where 'tis proved that the
Argle at the Center is double to that at the
Ctrcutnferenoe. The ufe ot thii Inftruimat it
very eafy i for you hava no more to do
' but to let the Index to the whole dfg'ee«
obferved, and upon the Ind^x graduated,
prick off the Minutes; This Protraaor
with Srales, ai before mentioned, ' with all
forts of Mathematioil InftdJments,are made
and (old by Benjamht Scot ( who fervid f)h
timi with Mr Rowley,) he keeps a Shopai
the Miriner and GJt^e over againft fxrtfr
Cbavge in the Strand.

Having now recommended proper Inftrii-
ments for protradling your Olifetvatioits,

{cannot avoid acquanting the Reader, that
he heft Inftrament to take Angles, is the
Theoda-

,..&„, .1,

Tlse Toung Sttrviyor*s Guide, 1 6y

XheoJoUie with Teleftope fights, as every

'Pra<^ioiKr will foon find the Advantage % as

fcst the plain Table, it is a proper InHru-'

ment for Learners of this Art to ufe it fof

a Imall Inclofure or two, fuch ai Gardens,

or GroBtid-pIots of HjoOs, fSfc. But 'tis a

Ihame for any Auill to ufe this Inftra-

rqeni tp Survey a GentleiiianB Efiate.",!

have Surveyed ^fl'e^thofe who have ufed this

lDl1rumen[,aiid I have increafed upon him no

lefs ihao^wo Acriei io. afield of 20. This

' was occ^oned by his going out in. fuch a

Morning diat was Fof g/, which -dampt his

Paper, and after he had workt about two

- Huuri the Sun ftion?, out and diminifhed

I \m plot upn his plain Table to the above-

i fnentioneii nf o Aqfes. Tha like Eftor ha»

i been cortimittcd by ihe Circum%encor,

^ 1 hope Gentlemen and others will take thisin-

- to their Confidera'ion, and not fufFer them-

felves to be impof?^ upon Yiy having fuch

-' Inftrumentsufed in Surveying their Eftates.

The Dividing (or runing off) both Ri^bt lined
I and IrrtguUr Figure's^ into 91 many partt u

you fi-tU M^nir', ^<pii'l or mequal.

\ . P R B L E M I

\ To cut off from a Triangle any parts,

« ttr* ^'- ^'^l* » ^^^ ifluing from any
^nglc afligned. _

.1

i68 The Touf^ Surveyor*^ Guith,

R U t P..

XriaDgUi canfiftirg.oF equalBifes^ani
and in .rhe -fame Pariillel are ^qual ^ there-
fore take 7, f , t» Cf- of the Line oppofife
Whe Angle \ draw a Linf, urtiich fliall \n-
nde. a TBangte. to.tontaiB the paiu re-

j^ig.ics. Admit ABC, tote a Triangle^
whoie. ^ part is required to be cat off,
with a Line iffiiing cnt of tlie Angle B, to
cat the Line AC j and then wiH Afi be ;one
fide of the Triangk : Tden' let rfit i part
of the Triangles Bafe be taken, wliidi endeth
in D, and let the Line BD be drawn, whirii
iiicludelh rhe Triangle ABD, which is the
^ part ef the Triangle ABt.

PS Q B L^ M n.

To cat off from a Triangle any number ^
of MeafureB, . as-^, B, 8, 3a, G'c with a
Line iflliing out of the Argle afllgned.

R D I E.

iFlrft Meafure the Area of the whole Tfi-

«ilgle, then multiply the fide pppofitp f«-

tht

TheToung Surveyor*! Gmde, 16^
'th« Argle afligned1>y rhe parts to be cut ol^
and divide the [»odu£l hytkt Pttea of the
wTi^e Triangle ^ the Qootient Diewi how
much you Oiall cat of^ to make a TcJangU
to coDlain (he required.

Bxamffle,

Figi 102. 1-et ABC b« a Tiiang> giveti^
and let the PropoHtion be to cut ^ S4

rti, with a Line ifluing from the A^gU
and falling on the Line AC, and malf
tog Be one of the fide« of the new Xri»
ang^e ; fiifl, the whole content of the
Tfiai^leABC* it found to be 3;^ Hav-
ing proceeded (I'iub, let 84 be di6 Ntmera>-
tor, and 336 fhe Denominator, wbich being
aUireviated thas, it< , -rrr. tt. t "rf the
Contem ; rhrn proceed in all Tefpedi as yon
did in the lad Problem, and you Aiall i^nd
the Triangle BCD, to contain 84. parts of
the Area « tht Triangle. AfiC» which wa«
leguind.

r Jritbmeticatly "performed.

Firft, The CoiHenfot Ann of the wholt
Triangle ABC, being^out)d to contain iT;6^
and ih< Line AC 42.} then fay by the
Rule of PrqjioKion, asdie whole Area^?^,
isto4a) foiB tbeleiTerArea 84, loafourth
Nuaiber, which is found 10 4. io the lame
1 Pawlle;,

] 70 The Tormg Surveyor's Gmde*
Parallel, which fet from C tourards A^ wbidi
falleth ID D: then draw the Liae BD,
which Triangle BCD, confains 84 gan8,.the
thing required.

P RO B LB M III.

To cut off any number of parts, as 20,
40. 60, fc. in a Trianglf, Propertional
to the Triangle gtven^, with a Line ^ral-
leJ to anjr fide given.

R U L E,

ftrfi, Meafure the whole Triangle, then
Square any of (he fides, in which jou '
would have fhe Parallel to cut 1 ihatS^aie
number multiply by the parts giwn to be
cut off, and divide the ptodu& by the
Area of the whole Figur^j out of which
Quotient eitraa the SqaitrRoot, and it
Ihews how much yoa ihall take of the fide
of the Triangle, to make a new TriaOgle j
with which Meafure found, fct ttfim B
to G.

Exam^

Fig. 103 . Let ABC be a Trianglt si«b,

from which 112 ia to be cut <wF with a

Line Parallel to the Xinc CAj the Tfi-

jiiigle being Qieafured, and found to be ^^6^

then

The Tow^- St/Beyer's Guide, 471
Aen put 113 over for tbe Numerator, 3i]d
3j6 ander it (or-theDrtiOminator; anil by
abbreviatiag.it, you Ihall find the fame, to
te t, th*n having deft^bed ihs Semi-Circle
on the Vne AB, divide iheUne AB 'into
.3 equal parts, and from arte of them ere£t
tte Perpendicn'ar DE ; then taJw the Jiftarica
from B to E, and fet (lie fame from B, to^
wards A,.which endeth in. F; by wliicK
poim draw a Line Paratlel to AC : S3
ihs Triple BGF doth contain 112,. m
was required. ' , .

^ jirh^metieal^ peffprpted.' "- |

■*B!^^ Square the'lMe BC'io, WWtfiihate^
400 i then fay, as ^6 is to 490, the Square
of that fide, fe is 1 12 to t;^ f, wfcofe Square
Root ifl Tif near rational j which is the df-

,. flimce from B to G i fb a Line dratfn from.

! 13 ■ Patallet to CA, you h^t the Trfaugl*.
BGF, ,which contains irs, as before. ': ..

>ff oj: n jH IV.

From a Triangle gtrei^ to lay tJie parti
-cut t^ in » Traperiant i if there 6e a Pro-
portion given between the parts cut ^
and the whole Figure.,

;. - . !

V

173 The Tmng Surveyor* i Guide,

i^^. 104. Let the Triargle ABCbegiveD»
from whence y is to be cut off in a Tra-
ptzium : Firlt then on the Line CB defcribe
a S>;mi-Circle i rhen divide CB into 5 equal
rarts, and of 3 of ibein from B, ered the

* Perpendicular DE, then felting' pne Foot at
your CompafieBiB B,<irend the other to E,
-which diftance fer off from B lowardi C,
which endtth in F^ bj which point draw
% Line Parallel to AC: So I include the Tii-
angle GF^ to coniain .^ of the whole :

. And confegueiKly th'e Trapezium ACF6
doib coBtain T of ^kefamrai was required.

Fitfl taV 4- froip the whole, the remainc'er '
-will be'4-5 then by the laft Problem make
tSe iTiiangle GFB to contain ^, and 'heo
it will follow, that the Trapezium ACFG
mufl contain ^ of the whole Tiiangle^which
was required.

vi ■

PROS llEM y.

''To' dividea Triangle, when the Lme
of Partition goes not parallel with any iide,
take ttuG iiiimple.

TlEw Toung Surveyor's Guide, 705

T'^ to^.Let ABC be a Triangle to bs
divided into two larts which ftiall bear
Proportion to one another, as ? and z, by a
Line drawn fromihe point D in the Bi&
or Line AC.

From the limited point draw a Line
to the Angle B j then divide the Bafe AC
into five equal parts, and from the 'third
point of Division draw the L*ne to E, Pa-
ratlel to BO. Lctfiij, from £ draw the Line
ED, fo fliall the Xnpfzium ABED be in
CoiHent as three to two, to the new Tri-
angle DEC.

I have now done with the D'.vifTon of Tri-
angles, when I have added thefe thre*
Advectifemenrs.

- Firft^ Yob ■ mnft be fute to lake very er-
i&Iy.thc di&ance of evei^.Foinr, wlur» a
dividing Line cutteth any flde, -to one of
the ends of. the fi'me fide, as in the Uft
Figare, thcj diAance BE and AD, which di-
flances beii^g applied to the Scale by which'
the Figure was protra£):ed with, will fheyr
^ at how many CKaihs and Links end, yniv
are to maks your dividing Line on thr
Field itfelf.

Second^ The proportions by which yom
are to divide, are not always fo formaily
given as in the former -Example, but ar^-
wmetime to be f(Hind out by Arithmetical'
working, as in this Cile.

I I Suppofer

JE74 "^^^ Toung Siirvsyor*s Guide.

Sappore a Trui^letof 6 Acrt«, 2 RMids,
^i Perches, mufl be divided, fo as ibe one
of ihe.2 paitsihall bs'^ Acnes ; Roods,
- oad ^ Perchct, tnd the odier oon&quentlj
I Acre, 5 Roods, and 26 Peiches; reduc*
liotli meafnA's into Perchea,tnd the one will
be 765, 3Dd!the other ^06. There Sum il
1C7I; which by their common meafuie be-
ing reduced itiro their loweft tf rms of Fra-
portion in whole nnmbers,wi)l be 5, 2, and
7, which {hews that the Triangle being di-
vided in 7 fgual parts, tbe one moft havc-
5 of fhofe 7 parts, and the other s. And
nb&ire that it nrili be fafHcient to find
ihecomrasn jneafbre between the Sam of
rhe Terms, and either of the Terms % the
Method whereof is Diewed in every Arith-
roatical Book for reducing Frmaioiis into
th«ir lowefl Tenni.

Tbirdy In thefe and all other Divifioos.oF
l,aiid, wiiete a ftrii^ Proportion td Qiun*
tiry is to b* obrerped, yon muft have re-
fpt& toriieJtules hereafter delivered. Bat
if there be Tiny ofeful Pond or Well try
draw the Line of Divifion ttiroagh ; hw if
there be anunufeful Pond, Lake or Paddlei
or ii there be any Boggy or barren Ground,
that muft be catlout in the Divi&n ; mea-
fure that firft, and fubftfaft it from the Con-
tent of tbe whole Clofe, and then fay the
juft Quantity of the remaiiider on tbar fide
that is^lxee fiomit, th« the other may have
fait

TW Vowtg Surveyof^s XhuJe. 175
his jofl p«t alfo, beftdes that 'which is
nfelefi. '

PRO B I EM< VI.

To cut ofiT from a Square vaj part pro*
pouoded in a Parallelogram.

RULE,

Divide the parts (n be cut off, by the fide
■ef' the Square % the Qiiotient fbews hour much
of the fide of the Square you (hall take for -
the Bifadth of the i?^rallelogram ; at which
diilaoce draw s Parallel Line 5 which QuU
include the ParaUelograiD re^nted*

ExamfJe,

3^i. 106. Admit ABCDtobe a Sgiiarc gj-
¥«», whofe iide is 20; from whence 160
parrs is to be cat olf with a Line Paralltl
10 CD, fo then CD makes one of the fidfa

(rf the Panllelogiam-, then work as is he-
)ore taught, and draw the Line EF? which
i}iclud£[h the Parallelogram CD£F, and
contains li^o, the parts rfaiired.

iVtrte, And if yon would have CHt off -',,
■^,£^c.. then yog (puft divide the SquartSide
to be cut off into thefe Pioporriooal parts,
^d.^by thofe pait3,draw a Parallel Line,
which wouU. have included a Parallelo*
I 4 gram-

17^ Tbe-Toung Sim}eyor''i^ CmJe*
gram to have contained the part* Propo»-
taonable.

FRO n LE M TO;

From an Imgalar Figure to cut off any^
parfi repaired.

RULE:

Meafure fo ntany f riarglea Ijirig next
to the part affigned, rili you have fomething;
too nnich, then by the firft and fecond
Problem of this part, cut of the overpluft
from the laft T'iangle, foftiU you haTe tk
figure to contain the parts rtqaired, •

J^g. 1 07. Admit ABCDEFG to be a Plof,
from whence 480 parts are to be cut ofT
with a Line ifliiing trom C, wd to be re-
wards the fide AB : Firft, let the Trape*
»um ABCG be mnfured^whofe Area is 370;
which added to 1 7.6, the Area ol the Tn-
aFgle CFG malceth $.06, which is too much
by 26, which 26 let be cot off from the
Triangle CFG, by the Line C b ; fe doth the
F:gnre ABC b G , contain 480, the parts re-
quired to be cut off

Note, This Problem is very rnaterial i»

the Ffad^ce of Surveying, in dividing and

IpyiBg;

Tl&ff Taung Surveyor's Gui3e, 177
i^jring oat Groundi, whether into parts
cqaal or uneqiial % which every Sorveyot
ought wtll to acquaint himfelf with.

For the better anderflanding this pointy
we will fuppofe a point given in the Peri-
meter of the Plot, from which the faid Plot
is to be divided ioto as many eqnal parts*
as fhall be requited t F»ft, Mtafure the-
Area of the wholfe Plrt^,~then divide that"
Content hy the number of parts (0 be cat:
off, and' the Qijotientihewethhow many
meafures each part Ihall contain } them
rut o£E each paTt Teverally, as^yoamre:
tau^t in the preceedjng worfc^ ^

P RO-B L EM Vm«

To divide a Cotnmoo-Field or FHObR;.
into as many parti as Diall be retailed ^
according to each ISaa^t Vso^xaoa. ot
RfcDt:

ExampUf I^

1^, ro8: £et ABCB£BGH£]r bta,
Common-Field or Failure, ia the Ufe- audi
Occupation of three Men, vis^ A,^C,.and!
it is agreed by them all,, that each Mas Oialb
have nts Staportion of- Gtaund hid ouf;,
according,to hia-Qjiantitj^ol Common ji^
tb*. fanft i^cr^

17B The Tintng &trve^'^ GiMefe^

Firfi^ Meafore the wtiole FicI;], add iC
will lie fouqd to contain 3; j^.;U. 1; P.
'>i' 7735 Perches i ihcnconfider Iww many
B^afe-Garec lher« are in th^ Paflure, and di-
yide the Q.uantif/ of th* field accofdingly
hy the rule of Proporrion, rhus j faying, if
tne whole number of BeaGi-Gat;! of A,B> C

five ihe' ivliole C^a^tity of Perdies in the
ield $7;5^ wjitit flia^ the ivimbcr of them
htloogiag to A, be, and the Anfver will
lie his part( and fi> work (ererally for each
Mans part : Bgt we may fuppofe them tbus^
•©■A,»8i7 Perches, to B, i7i6Perdiea, to
C,i202 Perches. Then to lay a\fi tvay
Mans Fiot, 1 divide the Figure by the Di*
felons afgrrgoing h-j t^ Lioeii B L,and
CMy which to lay out upon the' Grouad,
take- livmybLH'Scalethetli^nceoDthef lot .
brtween H and L, th«n meafiire out iks di~
fimoe on the Qiouiid from the Aogle^ £i
to L, atfo from the Angle A, Meafure oiff
^v^\6 to B, then draw the Line BLj sr
gain take from TOUT Scfk the duantlty of
XM 28. 00, which meaiure on the GrounJ^^
from L rp M, anfl there fet a Mark ;. and
an like ' manner M«afure frpm B to C upoi^
Che G;oBnd 25,^ 10, e,quA]l fo B^ UQon th9
pW, dn3wiQg |he;l4i^ 04^ So u yoqr
^ot divid^-.a^fiQiding: ti^«v«y Mansjufi
.<C^aiiUiJ; an4; ^ofortujOt

lUeT^Kg Suivgjfor^s GitiJe, 179.

Example II.

' Fig. io(). But fuppofe it W3I required to di*
vide thip Field between three Ferfons, viz.
A,B,C, according to eachMass proportion of
Reyt I As fuppof^ the whole Grounds to b^
so FcNjnds 9 Year, whereof A pays 9 /. B7 L
C4i' the Quezon is, . how many Acres,
Roods and Perthes belong to each. Man^
aKt:ordiiig to his Proportion of Rent, which
by tJie Rule of three argue thus^ ( fffifor
ji)lt 20I the whole Rent, give 573 y
Perches,^ (btitg the Contmt of the vbvle Fieli
in PercbeSj) what wjU ^'1. ^ive? w/z, 2581
Parchea,. or 16 A o R. 21 P. beiflg the pro-
portion of Ground beloiiging to A, for his
9 /. Rent. In like manner, & will have 1 z
A. z R. 07 Parches, being his Quantity of
Ground proportionable to hi^ent of 7/, and"
Cfor hi< 4/. )<jeat,^will have 7At,oH 37
Perdiss. 7hen to lay out theCe pacts upon>
the Groimd, oh&tV4 th« dizedwiu in, th^
dinner Example^

PROB I^b'm I3L

- To diwide » Field into three equal jrarrt-,
jBid e«cb Man to have the Begt^ of a Pbnct
about the middle of the Field.

Suppofe J;]g.i £0. containing' 27Acres i»tn &r

diiCdedbetweeathtee Men^ e|<di (o have 9

iBcrc*

off The Toung Surveyor's Gm4h^
Acres, and the Lines of Pivifion to ruot
from a Pood in the Field» To that every
one n^ay hare the Ben^t of ^e Water,
wi'hoiK going over anoihers L-iod,

Firft from the pond ® draw ILines to
•very Anglei ® A, © B o C, ® D, © E,
ind then la the Fjgnre divided into j Tri^
anglct each of which meafure, and put the
Contents feretaliy ^ which Content* n^ct;
4}1 into Pctchei fo will the Triargle,.

Eercbei^

Tlie whole Content hieing 4340 Per^
^eaor 27 Acres, each Mans Propartion
oeiiig 1.44,0. Frnm ® to any Angle draw
a Liof foE the firft divifion Line as O A..
X^eu cortiider. that the fii$ Xtiai^le A ® '
% is bu' 6?4 E^rches and the fecood B O C.
3?c^ both together but 1064 Parches, lefshy-
376 than- 1-440, one Mans Portion : Yoa ■
miiS-thtreforeoit o£P.from the third Angle-
C: D 376 Perches for the firftMan'i Divid--
ing line j which thn» you may do t The
Bale I^C is t% Chaioaii the Gonitsnt sf tbe-

The T^mig Surveyor^ Gmdk i84
Triangle 1238 Perches: Say then, if 1299
Perches give 18 Chains, 00 Links, what
(hall 57? Perches give ^ Anfver^ 5 Chain*
4$ Links i which^ fet from C to F, and"
drawing ihe Line F, 700 have the fiift
Al^ni part, v'rz.. A ® F.

&em^/^,See what remains of theTrianglci
C D 376 being taken out, and you will
£nd it (o be 862 P*rche», which-is lefi by
578 than 1440., Therefore from the Tn^
angle D O E cut off 578 Perches^ and the
point of D'.vidon will fall in G. Draw the
5,fne G,, which with A and © F di-^
vides the Figure into tiiree equal parw^

rR B t E M X:

To make a Parallelt>gram having an>
Angle equal ro any Angle given j and a;
fide of any Bergth, which ftiall be equal'
to Ihe Area ol any Right-lined Figure-
whatfoever.

K^.in.Le* ABCDE rtprerent a Fiel J*
of 5 jJOequal SidfS,. andit-was rfq ired to^•
lay out a Parallelogtam that fliall contairt
the fame Area, draw the priekt Lines E BR
and DB, then have ybu nMd« th» field to
confift ot three Tlianglw. Make the Tri-
angle a b e equal to the TliaPgU A^¥. by
Fnb. & Btvtde the Bai^ eb Inio two e-
quaL partt at Z;, and draw- the Line a z^^
«iluctL dindtt the Xnan^ e a b into two

1^3 The Tomg^rv/yor*j Guitff.
tqual pacts, vlx.. th; Tnafigle eaz ;;;: to-

the Triangle abz {hytbeerem i c^ at the pouit
9 make the Aogle n s b ~ to the Angle F.
draw n in Parallel to zb, and of equal
t<eogth to 2 b, drav m b Parallel to n z
and of f^ual Length to n z, then is the
Parallelograiji m n z b (iqual to the Xriat^Ie
cab. N^w becaufeit isrtq.jited thatap-aral-
lelogram ihould hare its i)de equal to thrline
A B, continue the Linen m, and make m x
cqal to AB.cotitinue (h<Linezb^Dd uiake-br
eqqal to m x, aad }oin, the Line x r^ from the
point xand b, draw the prjckt Line at plea-*
&re,'coptinue the. Lii)c o z to i^tiirfiA at
the point o, draw oy Parallel tozr, and
continue the Line m b to UDterfe^ at p;
making p'y equal and Parallel to b r, and
join the Line r y; then it the P'.trailelogrtm'
bry p, ei}ual to tne Parallelogram n m b z,
by Theorem 1 1. In like nranner make
t|ie F.traUeIogr^m py.q S filial to the Tri-
angle EBD-i likewift make the parallelo-
gram s q * h equal to the Triangle DBC,(hea
)vin the EaraUeic^ram b r f hbe rqual to the
Jtight-line Figure ABCDE Q.EF and QED.
If it w<re require^ 10 lay out. a Rlght-
^gled Faral1elcg[am . fqqal to the fame,
I^i^t-liqed ' Figure, aod ^e.Side fgual to^ -
the Liiw. AB, let the Right-lijied Figure
ABCDE contain 12 Acres ^ adding 5 Gjp-
phers t(y it, the fame Field willcontain
xj^oooo S^te Links ; X^t th; Liae AB le-
grcfeol

TBe T^ag Surveyor's ^'urdih i^^
prefent the Length of a Hedge given con-
taining 6q Chains 0% 6090 Links ■, Divide
1 200000 by 6000 aod Ae Qaotient will
be 2000 Liokp or 20 Chains for ihe Breadib
of the Right-Ahgled Riralklograoii foe
200a Links multiplyed by 60*10 Linki,
produces 1^200000 Square Links, or t^
Sqaaxt Acres^

2b reduce Stattat-meaptre4o Cufiomarj-imafwe^
and toe Contrary.

Although an Acre of Land by Statute i»-
to contain 160 Square Parches, of i^ feet
and # in the Perch ; yet in fome places of
the Nation, throngh Jong Giiftom, there
is at this day other prrcheg ufed, as 18,,
20, 24, and 28 Feet to the Perch y it i»
therefore neceflary to fliew hnw to teducfr
Sratutemeature to Cuftoinary, Cc.

Suppofe therefore you would reduce
Statute meaftre to Wxiod-land-meaferi of
18 Fe^ to the Pfrch, then 'fey,

M the Square ot the greater perch of 18-
Feet, is to the Square of^the leflfcr Pt:rch of
rS Feet aod i i fo is thf Content in Acres,
accojding to th« hSkt Perchj to the Coiv
tent in Acres ^ ^cco(ding to the gcestec

7

^4 7^ Tmmg Surveyor*^! Gai^g.

Let it therefore be required' to redtice ^6
Acres, 2 Roods, lo Perchei, at r^ Feet and
4- to the Pferch,. into Wood-hnd-meafare of
l3 Feet to the Perch.

F'lrJI, Tou mud obfeive (hat the Sgoare
of .16 Feet and \ is Dechnally 272, ay^
and the Square of 18 Feet is 324 ; then I
reduce the 36 Acrn 2 Roodi, lo Perches^
into Perches, which makes 585^, rfieh I
multiply the fame hy tlie Square of the
lefftr P^rch, 272. 25, and the Produft i»
r;92662. ;o, being divided by the Square
of the greater Perch. 524, the QnotientJi
491 y, "3 25, which is 30 Acres, 2 Roods, 2j:
Perches for tlic Jtfwer^

Btit fuppofe you would' reduce Wood-^
land-meafure into 9 atate-meafure, then fay^.

As the Square of the lefler Perch of t6^
Feet and 4-, is to the S^are of the greater
pitch r.8 Feet -, fo is the Content in Acres,
according (o.the greater Perch to the Comeok
inAcresi according to the lefler. Perch.

.^MC ta CJfJjl vp tfc CiAttetftofany flaty im
Jern^ Roodi^ mi Bercha.

H/. ii2i Admit the ft^owing Figtn«>

noted with the E^etters A^^B, C, D, E, I^^

G^H, 4 ^ tb&plotof. B Field, whofe

CoJttenti

The y^mng S««wj«ar/ Guide* i9%
CcHitent in Acra, Roods and Pcrdus is-
Rqaired.

Fi,fi, Then ( in aU fmh Cafes ) dirida
7oar Plot info Trapezia's and Triangles ;,
accordingly (his figore ift diifided into
one Trapezium, as K, D, P. I, and four
Triangles ; for finding theArea of all urhich^
begin with any one nrR, and multiply tlw
wniDle of the Bafe by cne half of ine Ptf-
pendicular , or {which » alms) (he wliole
«f the PerpendicuW, by the \ of the Bafe j.
the produd either of the Content of that
Triangle;, and then Som op all the Area's
of the &vsral Triangles to<u:iheE, gives yau.
tha Cont«iU of die whole Elot.

t^S^STk. )T"«i. D £ F 1-3-00
Triangles be. ^^^.^^ ^^p ^J^^^^^

The, Ace»d(th« W^ole Field. 1 2 --2— oi:

Sut the nuA exa0 way of all, i« to
moln'ply the Lei^rh of the Bafe of each-
Triangle, ■ by the Length of the Perpendi-
cnlar ^ the Strni Total of alt the Trianglea
being' halved, gives the true Area>of the
whpli! Field in 8^are Link*, (or Chmi^mi

1 8tf " Th« ToungSwve^s Guide.
Lhih^ which may be redocid it lafl ih
thefomer DireSmt) into Acres, Uxoie ud
"PtiKka.

Of la^^ imt KetfZtmi:,

A certain Qointity of Aorct being giren,
flow to lay om the £tnK in a Square

figure.

RULE

Asnez to ^Iie DBmber of Aceri given
fire Cyphers, which will tum ihe Acrfs
into L^nks.^ than from the Kun^ier tbui
increafed, eztmft the Square Root, which
fiiall' be the ficje of the propofed Sqoare,

-^ - . Eium^U. "■.,■".

Sappole the Kmnber ^iveo to he loo
.Acres, which J am to Jay in a Square Fi-
eace } Z join -to the-too, five Cyphers, and
&en it U looooQoo SftiR^ .Lttks , the
Reetef which is 31^2 neareA, or 3t Thuins
62 Links the Lergth of one fide of the
■Square.

Again, If I wen tocot otitof aCoTB-
'Field one Square A;ae,i 1 sdd tooaefi^
jCyphera, and then itj<jooooo, <he Root
■of whidi is.i^ Chaiaa \6 Jbinln , antf
iCboBthing more,, lof the Cdeof Ithe AcT^^'..

The.Th^ Survejt^^s Guided . 1-87

Uavte Uy out atrif given ^uwtky of Acres
« « PunpffsJigrwo, whereof one fidt it

R XT t E.

Turn firfi ^f Aa» into Links, t>7 ad-
^ioig ai befoise fii'e Ciphers 5 rfiar Nnmber
thus increafed,iUFide by the given Sidf^thr
Quotieat will be the other Side.

Example;

Let it be rfguired to by out too
Acres in a Parallelo^ni , one iide o£
nvbich (faall te 2a Chains : F'aQ to the 1 00
A<yes I add five Cyphers, and it is 100^
130000 , whid^ ( divide by 20 Chains^ the
Quotient is 50. Chains, -for the other fide of
the Parallelogram.

How to make a Triangle that fhall con*
tain any number of Acres, being confined
tcia certain Baff^

B V L S.

Doable die given number of Acres, t»
which annex fivtCypherSjWhich divide by the
Biie } the Quotient will be the Length ot the
^pendiculas. Tbisnecdano £aaaplr.

I 8 8 TJ» TUmg Surveyor'* Guidt.

Horn tty find the i^a^cf^t l^jmeter of *■
Circle:, vbich fiaU cancan cmj liai^er »f
Jeret,

u tr I E.

S37, as iinrto 14, fo will the Number of
Acrei given , be ta the Square of ibe V^t-
saetet of the Circle required.

Example^ ■

XVhat*« (he Length, of the Diameter of 9
Circle, whofe iup*rficial Content (hall be
Joo Acrei > Add five Cyphers to; the loo,
and it makes too 00000 Links, which
multiply by 14. it makes r'40000CQO j
whirh divide by n, gives for the Qjuotient
12727272 ) the Root of which is 3; Chain*,
6-j and fomewhat more And fo much Ihall
he the Diameter of the required Circle^

How to reduce a large Plot of Laoi
ar Map into a lefler Comp^fs, according to
•ny given Propoition \ £?" tfoirtr, how to
anlarge if.

Ftg. iis-TShe befl way to do thi»> is-, if
your plot be not too large, to Plot if over
ag^ by a finaller Scale ) but if it be large.

The ToUng Surveyor's Guide. 189
as the "Mx^ of a County, or the like, the
only way is to compafs io the Plot fitk
within one Sijuare, and aftetwatds to divide
that into as oiany little Squaret, as you
fiiall fee convenient. Alfo make the fame
number of little Squares up<Hl a Fair piece
t>f Paper, by a leiler Scale, accordiqg to the
'Proportion given. Tlui done, fre ia what
; Square, and part of (he fame Square, any
reuurkable Accident happens to fall, and
BOTordingly put it down in the leiTer
Squares $ and that you may not mifbke,
it ii a good way to numbet your Squares.
I cannot make it plainer then by giving
you the following Example, where the'Plot
ABCD, made by a Scaled to Chaini ia
ao Inch, ii reduced into the Plot EFGH, U
30 Chains in an Inch.

What has been hitherto laid concerning
reducirgof. a Plot Hxata a greater to a
IffTer Volumn, the fame is to be under-
flood vice vetftf of enlarging a Plot from
. a It^Ter to a ^eater. But this feldom comei
in Pfadice.

Knowing the Content of a piece of Ltnd,
to find oat what Scale it was plotted by.
4 Fir^, By any Scale meafurc the Content
of the plot } which done, the Proportion is
as the. Content found, is to the. Square of
the Scale it was tried by ; fo is the Content,
to the Square of the uue Scale it was plotted
by,

Examglfi

• 90 Th Toung Smrveyor's Guide,

Admit, ttiere is a ^ax of a jnece cf ]|uid
-containing 10 Acres, and I meafure it by
a^caJe of 1 1 in an loch, find it contain
12 /teres.

Then I fay; if 12 gires for its Scale i^j.
What fliall 10 gire>

Mfver^ 10. Therefore I conclade jt wai
Allotted vf a Scale of lo in an loch, '

^ I -N ^ S,

APPENDI.X.

the Totmg S^wgor's Guide, i ^i

Ion? to take the Gremdffjot :
^ofahy dty or Corpbramn
; bytbtTheodolkeorDegreer _
■ on the plane Table.

FOR (he potfOTimince of wjiith, Jt^ill.;
be neceffary foF th« ^oung, fiijHvey«r to '
provide himfilr of a Cheutt thatis: Je'f'oot
long, contiioing ;o Lmks, and esch Vaik s
Foofi foB all Ciijes are befl Iwd dotvn by

H Scale of Feet: It will be convenient . tbat
he bawi b Rbd that is 5 'J^' Jo Fopt: In.'
Lc[igth,and tolie fDbdivKli!d-ipto.F4et;'3:his
Rod is ti&tate the ^DSf^ofthtiHotifM OS/

r borti 5de8 your Clniii, aa.youmeaifiirealaag ;

;'the^»eet»orIjiaefi. ^

■93 ITx Tmmg Surveyor* s GuiSe,

Exampla,

iji !Rg. ^. ht i part-of (braeCitj, and
yoa are ivquiretl to t^ a {jroQtKt-plot
thereof.

FiHl, Caufe two Men to ftand, one A
B, -Hd tbectber at- F ^ tittfi .facing yoqr
laftironeof at A, Iayihg'tlie*Iiid«z ,v^
ttk Dntmetei:, torrf it ^btsuMmtil ttvoogh
the S-^ts you efpif the Man at ¥ ; thea
fcrew your Inftrument faft, and direiEt your
Sights to the Man at B, and note the .degreei
cot b^ the Index, which let be 9; deg. and
30 lAm. Not« this 9; deg, and 30 oiitk
down in your Field- Book,' as yon did when
Titu ineafnred the Lane-, then with your
Rod nipafure yoer Off feti both the Right
and l«ft, a$ yoa did in meafuriog the Lane
alfo ■, which yoa will find to be to the RigTtt
5 Feet t then with your Chiin meafure to^
wards 8, and at ^ Foot difiance froin A,
TOO will have yoar Off-fet to the Lefr (o
M 7 Feft; 'Tibte botfa thefe down in your
Feld-Book orEy&d taught, which is beft tore-

refent the thing 1 theruneaTuring on rou!»d
you will find that at 47'Feet didance
from A, you «il1 have a Street both to the
Right and Lefr^abd the Oft-fetTo the Right,
will be 10 Foot, and to the L^ 6 y note:
thefe down in your Field Book or Eye-
draugftt i then ftill miafurtag toward B,
you

Tht Toung Stmieym-'i Guide. 193
you will find ihat at 90 Foot diftance
from A, yoB wiil haffe an Off-fet to the
Left that IS 5 Foot \ note thia down in your
V eld Book, alid at the fame time yoof
Off (e« to the Right •'ill *e 1 1 Foot j note
' Hiis doifrftalfo i then come to B, where one
of yoOT Men Sood, and by ipearutlrg with
your ©lain, you will fiD^the diftante be*
llten A and B to be voo Foot i then pla-
ins your Inflfliment ?t B (cauTmg the Mm
that «bii(*rF, <o flsfid at A, lo fonn as
you tot^ your Inftiument up from A )
htyilig your Index upon the Diameter, *unt
your Inftrumenr abotii until yju through
ifc'Sighn i:fj?y the Man»t Ai there maka
Wtmi InftKiHieM ftft. anj'caule theMan
filal flood at B, to go and (land at C , thea
afr^a your SisllH to C, and note the deg.
cnt by thelndel, wtiich let be 140 deg. then
withyour Rod'meafurethe Off-fel both to
(he Right and Left, and you will find that to
(heRidit is 1 1 Foot, and to the Left 8 Footi
their ^Mfe your Men to meafure towards
C, 1h as direa a Line as they cm, and at
61 Foot diflance from B, you haveaStreea
both to the Right and Left i then meaTiire
the Offfets, and you will find it will ba
a Foot on both fides the way, vis. to the
Right and Left, at 120 Foot dilbnce from
B, the OfFfet to the Left willbe found ta
be 8 Foot, and at 127 Fool difbnce from
B the Off fet to the right i< 8 Foot alfo ,
K thep

194 TbeToung Smi}ey9r^s.0Hi<k-
tlifn youwiU find you jnbc^M^tflQi tbcp
table a ftfonrogoindfand tit<@« j^c^an-
oibttto ft»iul«tDv plvx 3r4of ?#^nnii
atC, and fay ithe rintkzltaereof «BpBMlif
•Diitiiietflr^Ttuinirg it abviit.'tiUl^pifgti th^
Si^hrs you-cTpifc ttie'MBtfatBi:tfta<if(^*V
■yourbmruqiar/afi ^ theh dii^^ 71041 Stehcf
■to ibe Man « D, .abd/tfw tn^ltiE wilf-l)^
found to cut ttoo-degj and^if.you/inea^ufi
wiifa yon Kod.. the Offr^flp.tbfiTiglu.j^
(he 'wiie tiint, ittirilL'be.fcmiid^rfd %f^^
.'Foot^t then ineifiire ttith yi6ur;;Oi|ait:^ to*
wards D, and at gFootdi^n^^ ^em C^
the OfT-fet to the left will be foqfid.'lp'be'p
Foot; then jnesTuK on . w^Ji; yjif^ piui^
and you will fibd that at ^4' j^g^f^l^piis
framQ ttM0fffettoth«dercis4fFaat^'||f

iS4rt'a«tfra

75 Foot the.diftanc£>of QS,
the right it .12'Fcut ii.tbea^piacF.i^iml
flniment at D, and catrie a Afa^i to^pa^ffa^
C, anri another at £^ and lE^'ipg^tneJqd^
of the laflrunientiipoo ^ .Piap^af;.,, jmip
it aixiut till tbfough.'ihe Sifi^ -3^ ^U^
the Man at G t, thettwak^ f(m.}^^mitn^
iaft; then diretfl your ^ghMagw^ W§tM
ark\and you wiWrfuid that th« ^dex.V^tqit'
icodeg-ihen withyonrRodjineafiire thtutf.
fet to t1ie tight, and it.itfiU be iqurid ^ b|| ^ ,
Foot,and tiileOfF-ict to the-)«ft,ii ;Foot ^fi^tf
wiill 7tnti:<^1^in' ineafrKe; tourardt^i^.jttiff
at 4T Foot aiflance from D y.o".wJI^^ l^a^^
a Strett-td.t he right and , lafr 5 4fc^ nia^u^
itig on cewatdi £, .you will ^nd that at

■ The Tbung Sttrveyor*s Guide. 195
•'91' iFoBt'diflatice"ftotn D-yoU mflKai'e An

Gff'fet'ia'ftdl^iefrt^iif-jFoor andthewhola
'd!H»n<(« b^lwe^^^D and E will 'be found
' td %fc ic<3''F£K?t','t!ifen^ladng Vcur Inftfti-
' flt'E, caufe «' Man \o ftand at I), and an-

tJther ar F, and lay the Indej upon the
■'Diameter, -and-tarnyoap Instilment 'alnjiit
'■flB'yfeu'-ef^ie the Man it D' j ,t1if re nlat«
■'faftj-Dorlnft^unifrrf/ana'direiayobP Sight*
' tojF'^driote (he dtgrci-'scat Ijythe^fn-
?deijtvhifch'^«?ifl '!« found to 'be a r'b deje-
■iheii *ffith youi'Rod mpafure rUe Offlfct to
'the R%ht, apd jt wiM be foitnd*' to be, 7
. Foot i tTiiefl with yonr Chain inVaffif e A-
^v^fds Fi^ aUd at! 9 Foot d-rftafnce fii)to E,

■imil I-«f( j W(^Mei;ar^tb^ (ifaWifafeT^I
'lie"Fbilnd to ht to the RikHf: 7 T^obr, sllnl
■ to 'the- Left 12 Fooci flrl^ Afsl%tn^ (b-
. wards ti fm'lViW 'ffiid that w '-70<^o$i'^.
-flance firpiit P;' yoiir lift'Satftrf, 'Jdni Will
-fifl* tbe-Offilt to tht''t.d/t'w'be'7¥6of,
■anfffe CMfftt.tb'tKe %?ic;ii.W ^F6r*
-^the Whfclti.^iftance betw^eeriE^j64''f h'f r
Foot, then flacftig ybi]i::''inftftiriKhe'at F,
caufe a Man to ■Kand ' aV A, and anoihartj*
flahd At E>''ihe"iflace ufhere, yon J?R harflfc
-9rttion,--thetf'T3^^ ■yout.liides iipon tH«
Ojamtter of yofal''llillriiiiiehr,.toin the'-ftriia
abt«\tuntil.rtirpughM SlgliW'ylju eCpie tlltt
'MajJat'EV 'th^-c make ybur Inftrmnent
'ftftj aocf dJreti Voar Sights' to ttw Man
- ■ li» ««

if6 The Teamg Surv^r*s Guide,

that ftandi it A, ard 70a wilt ^od the- In-

dfZ will cut 74 deg. and 30 iniit,thai whh

your Chain DKafure (owaids A, and at S

Foot diflaoce Tiom F the OS-^k to il|e

Right will be found to be -5 Foot, and to

-the Left 7 Foot \ then nieafuting. on to-

-watda A, at 67 Foot diAance fiom F, yoa

will have a 5<ceet,both to' (be Right and

..J^eTt } jind Hill mtafurirg 00 towards A,M

1 123 Foot diftance from F, the OfT^fet to

-the Right is 4 Foot, and to the L-ft J

, Foor, and the whole diftance between F and

Ji. is 129 Foot, then have yon done with

.^e Obfeivaiions in the Hign Streeti.

Nftfy Vou are to fet down all your
' Ohfervaiions at yoiigo along in yoor Ficld-
' £aok or Eyc'draugbt, which is beil. You
may make an Eye>draughr thui^ Firft go
along the place that you intend to take a
Tlot of, and draw Lines to imitate the fame,
-with (fors Sireetsif there be any, noting
your Sratioos therein by (his Maik ^, ; fet-
line at every Station the Angles oblerved,
:ana the Off-fet oh either £de the. X-"nc, as
you find it to be when you take theiii,andthe
'jLngthoI the Lines betwf«n Station and
£iation,and ly this means when youcame to
^protrad your Woik, you will have a leprt-
.ftntatioii of all the Work that you have
,takrn i but if yoB fet down aU your Ob-
liervaiionsin your Field B^ok, it will be Uf-
>eflary to£etthein4owiiiii auBDeruul forjn

Thf Toung Survefor*s Ginide. t^y-

nfTtbU^ObfenutmttMktawbmjniiwtiit abtut the
'High Streeti. ,

■ot-&

S»Oi"H

A(to.|DI/l.l

X.

X.

00

i m.l Ftii. '

SI

1®4

JS 30

■s

at-

6 from A

00

7

«—

47 from A

i-f —

— 'i Street R.*L:

10

<9

•t—

« from A

5

'•■:

"o from A

\1

00

3eB

140 60I00 (from A-

n

8

at—

''■feomBaSfireet
iotheR:&l.

9

9

■«r-

,

"ofeooiB

.0

8

;»t-

■^TjftomB

■'.8

00

a.ec

Kut <K

>»W*onrB:

8

<?o

,at-

f4-

Froni C ■ '

00

9

at—

00 o<

fromC

00

4

at—

7?

from C ■

12

00

4«'C

100 00

7!

fromC.

9

II

at—

41

frornDsSffft
'0 the ,R. » L

■ J cot

,at—

• ■' ■

91

From R '

CO

7

J«E

2tO 00

roo

From D

at—

9

aStreetR.&L.

]

12

at—

i:

from E '

7

< aF

H t°

fromE

;

»t-

8

rom'F

7 ■

at—

«7

iStreet R. ItL

at-

00.00

.n

PromF

4

T

K]

uviog

198 1 7Tfeit^> SWrt«^f GWiift.'

Ha^ifJg'thttsrtkeil j^oiir High Streets, ym
m m ill the like mimieiJpttce^ widi ttw o-
thef fm^l Streets and LincBi. with feveral
Boug^ and Breaches, noting doftntifymrtj
Ej,e*4raijefit^f^l''i' 1* Booiagaiuft evtiy one 1
of thfin, Ifhe'OffreTsTq the RigTit dr Ldt,
according; as yoy 6ad<hamon either fid« |
of; yoqr dhain. ,. - ; - ^.. ■ p :< '

^o/e, 1 1!^'}9 tfnhei^.yhii. t^e yoot| omw
Sft^'et^itwill b9Cpn;v«Di«Ki8often ^»yM '
-cdm^ iijgp^ftany^^Sireeftotakc ^Sigbt .
dditfn iy, iand no'te^he't^bce oc tpatk t)^t '
yifu ti^keJo, and tJift,pl2csdf fiandingwhra ,
ydfi uke yoHi Sij^ht to ;fi>y Mark thsA is la
tht ao!^ Srreets ui jour Eye-dnughB wilh |
thUMvkj0, andfq^by <h«einean< yqtiWfi] I
know wh4ce to p|tc« y^tiriaffaanent'^^biil
r^u'&fl^to take, ^ecroTs Streets-,; your |
li^h Streets and; your cipfE Stt'Dis being ;
trai^ t^en, in th« next place you are ^otake .
the .tntafure of the Houtes to the Froat;<and i
lit^ifc t^e deptfaf o^.every oneof the^and '■
wjth jrou^ Red. or' feetfil talje the Ptott of •
yqur Coutts and A%ys, fiifl 5y drawuigttn '
Eyc-drau^ of tJ^m, fetting- upotf et*/
Break or Retuni.tfiereof the meafure you
took with your Rod % and id fo doing, you
will find ifnoharj matter To protia£t die
Tame after {you havjp fMtjiiftet^ both fides of
*very Street ^ /or you wjll;haTe the ReiffC-
. -fentation of ever^ Couft ^ad; Alfey [n lt&
proper pl^. ' '

II

CHAP.

F

i .-.'; i!.:!l ; rll,M-l ;ii.')ii',(!j . 1 .
jKioi^n i:r" J H V. Ill'; . )1 {•\'. ;■ .

.srav- 'if. -' >^"a iw- '■■■'■ ■■■'--;

Hmd tavUttiMa HoK.i'Uy dom> my
\'^;qblir^t0fM¥tkmding to the

K,) .iil.I 5:i: ,;:■!, .'.;,■ , ;;

>IHIj hii*itie-"prtlnded'yodr<elf of .good

t'TjM tt :la(glk| t«ii«utAr« tte Liu

f^())H^iWl(i[)oWlltt'{li)llU,[i<ara TantPl^-
rfMtor ftmiiiH)! liKW«rAaiha>«iln
^t!^>cUtl»fintt'AP'^' dun'&ding byi
3*«u^Fi«U>II(Mc 01 Ej'e-dniBbt tkat th*
An^l^eKctVMtur'A, vit.^i Org, and 30
il>ii<j'«^t ^'ti^ fo arin. •( ytiut Pio>
tfkWI^■ltlft•'«'Mi•Ujl»nddiltal the Liu
A'^.lrf W^il!; oHn. fiildit^g.Biro Hnn lh«
']aiBthitfiA3>-^aa't)ba'ftot^ nilea icoirotn
off yfbrBoAe pf iqtnl Parts, . and place it
fnnbA'toB^ then plaoiDg the Cenrer of
your. Pr^airidsr. on ine-Jsoinc B,- torn ycuf
enmriaiir Ibodt tlnUI thoCin^ A£ therAjiC
laJinSl^iqlOil Hirlait A b hfidrawn ,
Ibfa-' Aiding 'that: tha Angle, obieived at B
ttw'-^'^adeg-'«gaiBft'l4eof yoof Pcouadof
make a Nbuk with y6ot pcolra^iqg .pin^
K 4 ~ and

300 The Tou^g Swveyor's GuiiU*
and draw the Line B C at Itngth ; then find-
ing atfo that the length <^ B C was 1 27 foot,
(axe 1 37 from off yonr Scale of equal ^vtb,
and place it from B to C j. then ujring the
Center of your Protni^tor upbn the point C,
turn it about until the Line A B thereof lie
dirrdtly on the Line BCUftdriwot thni.
iuiding by your Fleld-BoolE or Eye;di;aD|bt
tfiatihe Angle obierved at Cwas ioodeg.a*
gainft 100 de'g. ^with your pH>tiaffing*pin
make a Mar}^ and draw the Line C Dal
Irngth i then Ending that the iHigth of the.
Line waa 7!> foot, take 7; foot firotn off yoor
Scale of equal part»» and ptBC« it fxom C ta;
D ; then lay the Ceftter of yota Prptraao>
uponD, and torn it about qotil die Live A
b thereof lie dircaiy oil the Line D C laA
^awn i then finding by your Field-Book or
l^ye-draughi that at D you did obferve an
Angle of 100 deg. therefore againfl 100 deg*
of youf J^otiaaor, iriib your prcttrafiing-^
pa make iJOixt, and dnv the Line D^
at lei^ V then finding aUo ^ttlM InogtV
of your Line D E wai too fbbt, take looi'
from off yoor Scale of equal parts, andplace
it frpm D to £ { theii remove your Pn>tra6tor,
and lay the Center tbercof: upon the point E,
and finding by yonr Field-Boolk the Angle
obferved at £ was 310 dcg. agaxnfl'iiode^'
of yonr Protra^r tiiake a Mark with yoat^
protrafUng-pin,' and draw the Liiie 0^«al
length i then finding that the length of £F nraa
83

The Toung ^atje/or's Guide, aoi
83 foot^ :take 8j from off yom Scale of e-
qual pdrtt, and place it from £ to F ^ then
placing the Center of yout Proirador upon
the point F, turn it about nntil the Line AB
thereof lie diredly on the Line EF lift drawn;
then finding by your Field-Book that the
Angle obferrsd at F was 74. deg. and 30
nin.,againft the fame d^. and min.of year
Frotra^r m»ke a Mark with yonr protrad4
iog-pin, and draw the Line F Aj which it
you have protraded right, will tall to fas
cza^ly 129 foot; then have yoa [tcotnfieil
yotir priocipil Lines. Kow bcgifi to pro^
oad yoar Off-fets thus.
: jFir/, finding by your ^U Bookor Eye-
dfaogfarthat at your firft flation A, the Off*
frt to the Right was 7 foot, take $ foot from
off your Scale of equal parte, and plsoe it
fromAtoa-, then finding alfo that at 6 fint-
diftaace from A, the Ofi^fet to the Left wa»-
7 foot, take 7 foot from off the faiae Snle.
of equal pvts, diat ycm protnficd-yovr'
principil Linn trom, andpfaiM it-froia jL^
loo ^tben finding that at 47 foot diflance
from A, the Off fet to ih« Right was to
foot, iake 10 from off yoar Se^«f e^al!
pvtt, md plare it fioan « on the Line AB« ■
to 2; asd draw the Lrae a sat lengths .
ibcn finding alfo. at the^fime timetiw 0£h -
let to the Left »u 6 fool, take fr^em off ^ '
your Scale, and fettin^^one pcrini ot
your Cempaflec Jn^»^ on the Line AB^-
vith. the other jnake a Mark on the' Left
K 5 , baa :

los . IhiTaiHg Surveyor's Gttide,
fund of t^e Lise. A B, and dl'sw a Lioe
froJn 9 tb rhifl r laft l/imk 'made ^ . ithen br*
erafeyoli find by- ^ur Field- Book ihac aft
t&e Jal} Dffftfts dmre wis a Sunt both to
ths-Rishtaod Lert^ yofx muftmakc a Mark
^■fignirjr^hefaiiie^i then findiag by your
Fiel^BM^ thai at- 9{z foot ilillanec itoOi A«.
the OiNetto Ihctcft trai $ fDDt,lb«[t;$&oa
tafceHfl;fraiiioff7«T:JScAleof«^lpafts»and
ftniag «ne//cbt of ^r Cmripaues in-rhs
piinC /, with the'othw tna3ce s fmati MarJr
to*^ Ldt tMnd: af the'Line \AB, and
itXK^A Luv froiil the >SlKit toi ihis Maric^
the Offfet to the B^kt atthBTarmej fim
waffliQ-iiiiff:^ 't^S 'thtt -I's fdot. firdm ^oiF
7^btJr'S<3i]<t Bt]d^feltiigi:oiie.foot of 3rotir
€&ailM<]>ffmthe,pDiDt; with ths olth«t tmkA
d'Msr^ on the R^t fid« of the Line :AB,
diȣdrilw a Line Aram the Street itirthia
MvkiUS «riad« -, ifi^'Bifdif% itet vbyoot
«ki8n!i»;i'yed1iaa> ifae£)ff&t:i«*he.]tiehe
!fr-^t)->fisk!»:q[rA^inioff'^o«r< Seale^ of

.-paflcf' i^ tiiei p&^l^ B; .wah theoiher^ ma^
«'Maf4p oiftfiS ftigbP-hana-iTde 6f thk Line
£G4^Hf 6lili6tw thefanu timeitothe lit^
VM «i':aorv) «ikt i&^fbot fraiq loff ^yuw
ScaU of equtl ^^ana^and fitRibg.' aae Jose
c^'^eQr6«ttipai&£aintlKpdiflt£, WJihthfr
liMiemiddct a:Maik'0h the: Left Iid4 of 'the
KinfBe'i then folding by yom PieM-Baolt;
or £j«-^augfit that -at 6i foot, theOf^
// ,:i i.; : ..:: .: : ..-■; ■.■.., um

«tt(^tlte m^ apd Left vac 9 fooT, tske
^irQcntCj^OW^cale of equal parts, and
^tring^ one foot ol your CompaiTes in the
point p, with the other m^e a Mark on
both fideathe Line ^ then draurLinet on both
fidei of the X^ioc BC, Uom the Mac^ made
on. both fidei of the Line at3, to ihe Marks
Ia$ made \ and becaufe there is- a'Street «•
the Offfei lafl taken, make a Mark to
lignify the fame at 1 20 foot diftance j&om
b, the Offfet to ihe Left was 8 foot j taka
8. from off youf Scale ot equal parn^
anifetting o|k foot ot ]ra«c Conip»fr<4 is
the point V, with- the other make a Maik>
on the lAi fide of the l^nt B C ^ and draw
a Liflfl from th« Street on the left fide of the
Liae BC to the laft Mark Qiade ^ then a|
yourfUtion C, you bad an OSTet to ther^
Ki^t of 8 , foot^lfo ) take 8 Tioin oS yoor
Sealepf equ^ 'pactt, and rating dds foot
of; jTRur Cam^uOlei ialhe pnin« C, with the
othnr nntlEfe ,« Muk^oa the Righ^ iide of ths
Lint Be, and draw . a Liae from the Mark,
tlial you mada forthtStte^ oathe Right
fid« vC the LiM BC, through the latt Mark.
madeat Ungih % then fuidiii)} by yotirFieU*
'Sfoak M Kye^nneht, that when yoo had
db£«re4itlM^&0gW'a« 0, yo^ had an Oif-fet
•o^beiRisbtaf a foot, tak« 3 foot from o£f. •
yotv Scale of rqal parts, and fettiog one '
ipot. (^jfow .Compares in the point C^
with Ok drtwi ) «»b I « iM M ^ ftjfhi..

ao4 The Tomg Surveyor's Guide.
fide of th» Line CD I you likewife imd >t
8 foot diftance from C, yoa had an Off>(et
10 the L"ft of y foot i therefore rake ^^com
your Scale of equal parti , and plating ope
foot of your Compafles in the point X, with
the oth«r make a Mark on the Left fide of
the Line C D ) yoa will Hkewife find by
your FieH-Bookor Eye-drarghtth5rar ^4
foot diflance from C, yon had art OSktto
the Left 4 foot » take 4 from oft' your Scale
of f q'lal parts, and fetting one foot of your
Compaflea in the point Z, with the other
make a Mark on the Left £de of the Line
CO, and draw a Line from the Mark that
was made oc the Left fide of theUne CD,
at X, to the inark laft madei then by your
Field-Book y 00 will find that at your ftg-
rion D, the Off-fet to (he Right was 1 2 foot j,
lake 1 2 foot from off your Stale, and fel-
ling one fcot of your Compaflesin the poinl
D, with the other make a Mark on the R^t
fide of the Line CD, and draw « Line from
the Mark that was made on the right fide of
the Line CD, vis. at C to the Mark latt
madej thf n findirg that whffi yon obfeived
yruf ^rgleatD, you had the Off-fet ta
the Righr 9 foot, and to the Left 11 foot,
take 9 foot from off youc Scale of equal
p^rts, and placing one foot of your Com--
pafTes in the point D, with the ether main
a Mark on the rrght fide of the Line D£^
and take 11 from eff the fime Scale, &t>
ting

„,.,,.„..Coc»;lc

TheTtmngSwwyoT^s Guide, aoy
ting Mie foot as before in O, make a M»k
on the kft Jide of the Line £>E with the'
other { by your Field-Book you-will find
that at 41 foot diftance Irom D you had a
Street both to the Right and Left ^ make a
Mark to figntfy the fame : Likewife yen
will by yfinr F.ifId-B>ok i]iid that at 513
fiiol diflance from D, you had au Off-iet to
the Right of $ foot i take 5 trom off youf
Scale of equal parts, and fetting one lootttf
your Compares ia the point Y, with ^ o>
ther make a Maik on the right fide of the
Line E^, and.diuw aline horn the Mark
nude at D, v on the rig^t ^de of the Lint
DE, fo tbe Mark lafl irade at length, until
it doih'iat^rfe^ the Line that was drawn on
(he right fide of the Line CO: Yoe. witt
find by your Field-Bookthat at yonrStatioa
E,.the Offfet to the Left was 7 foot) thi»
7 foot tike from off your Scilt ol tgiial parts^
and fetting one fobt of your CompaiT^s in
the point E, inth tbe oihrr make aMaik on.
the left fide of the line DE, and draw a
Line from the M»k made on the UU fide
of the Line Dti, at D « to this Mark Jaft
drawn at length ; yr>a will find by your
Field'Book that at 9 foot diAaeee from E
towards F, you had as Ofl-lVt to the Right.
y foot, and to the Lft liioot^ ihrretore
take 7 foot from yt-ur Scale of fqual part%
and luting one foot cf your GompsjTs in
Ibe poim H, with lbs ouux oak* aMaijc

oD thi righi ifide ijS the Lide F£ ; andMin*
wjfr take 1 2 from the fame Scale,, and : p)a-
dng one foot- of ytut Cdinpii^s as b<iare,
in the point H, with the other make a Maik
on the left Hde of the Line iF, *nd draw a
Line framthe Msrlc that wai made oq tbt.
left fide fif the Line DC, at IT^ to tbis'
Mark laft 'laade } iheu becaufe thefe two )aft
Off-&ti wsrev the Coiners of tWo Stcceu,
itukc a Mark to fignify the fame } at 70 fool
dfffautc* from E towards F, the OR- fet to
the Right was 7 fjot, and to the L-ft 7
&ot'alio, take 7 footifrom oif jrour.Scate.oi
equal jaitts, and placing one fool of yvat.
0)mp»ires ill the pant K,' with theothdr;
make a Mark on earh £de rl the Lin^ EF,'
and draw a Line frokn the Mark that w«
made on the right iide df- the Line EF. tit
H, to the Mark that was laft made on the
p^kt'^e ef the'LiihejEPat Ki} ^Bd diaw.a
Lmc likewife'ff dm the Mark ihatwu made.-
au the left iide of fhe LoierEF, at H, to
the Maik that wasi laft jhade oti the Irfr fide
of the Line EF, at K ; then by your Field-
Bbok you will' find that at y^r Station F,
foot' Off-fit to ttie Right was 5 hot ; take-
^'from year Srale of equal parts, anid pk^
Cibg'-one fdat tif yBarCompafTts in-.the:
point F,' with the othei make a Msik oir
the rigHt iide -of the Line FA, and at 8 fool
diftance frnm F, you had al^ tbeOfF-fet i»,
the Lflt 7 £e>M ) taJse 7 fmmoQ-ytnir^ak.
■^■■^ of

of f!(pisltp4Kl^>iaBd'<pItcaigiqn«foOTof^ur
Compaffi«^a the foinr N, with the other
make iMirfc-6n the I/sft fi.de tjf (he Lid*
F A. At 67 Foot diflance from F, you had
i &ieet to the Right and Ltft ^ therefort
makeaMarkto Hgnifie the fame} at iz^'
foot diftance (mm F, towards A (by ytnif
Field-Book you will find) .you had an Ofi-
fitt to the Right 4' f6ot i take 4. from oS
you^ Scale of etjQal parts, and plu:tng oda
foot of your Compadf s in the point R, with
{he other make a .Mark on ^e right iide
ef'tic^Line FA, anddrawa Line from the
i/bfii that was; made on tbe right fide of tfab
liine FA, at thrpoiat K, tothe pomtthair
^shft- made,, fo that tbe Line whidi yad
dravr may ioterQd the Line which isidrawn
(HI the light £de of .the Line £F, and: tbs'
I^ine that ii ^rawn on the right iide of the
line AB^ tJien at tiieTame timeyoahsd:
M OlB&ttatbeLeft,-, of 5 foot ; take ifl
likewife fronk yducSc^eo^ equal parts, and!
friacing onfe' root ofyooe GoeapaiSfit in tQ£
Boiot R,withlhe oe^ipt inake-a Mark on the:
Lft fide of th«LifteFA,ard drava Linefromr
^e Mark tJiat was mtdeoDth^kllfid^Dptht^
lJinEFA,BiNjto tbt Mark thiittarailBft made*
«n3hs;left iide of ^fadKLnibatiRv t^Koh^yft:
Tou mnd^ a> end of protiafiiagi^loub HigH-
Streets : in the (ame manner, you muR pro^
traa your fcry-Lanea and Streetp. llda niuft'
likewife deal fb. witb all AUejsthat lata.
Tbocoiigh farea. ^[ow

ao8 The Toimg Survejf^ Oai^g.

Ynut Street! and Lan«t being ttnis pro-
traded, 70U may proceed to theprorrading
and laying down the Groand-plot nf the fe-
Teral Hcufes thereon ^ for the doing ot which,
it will be ronTenient that you have a finalt
Scale that is adiially divided into 50 equal
parrs in an Inch ; then laying your Scale
a long by the iide of the Line e, and
againA the meadred breadth of each
Houfe, with yoor protrading pin make a
Mark or Marks } then lay the Edge of your
fmall Scale along the iide oi the Line e S,
and againft the meafureof eadi federal Hou&
that ii thereon, with yoar protraAing-pin
make a Mark -, then lay jour fmall Scale a-
long the fide of the line SQ, and finding
by your Eye-Draught that there is a Coart
oc Yard, fiifl make a Mark againft the
meafare ofthe Teveral Hoofei until you con»
ta the: Court or Yard, and then mark oottbe
bfeadthofiheEnrranrc thereof as you did (he
breadth of the Honlrs^ and likewife maka
Mifks agaitift the breadth of each Hoaleon
the other iide of iheCourt alfo ^ then laying
yoat finall Ruler or Scale -along the fide of
the Line Q.O, againfl the mufure of the
breadth of each feveral Hotife, wrthyour pro*
trading pin make a Mark. Having thus laid
down the breadth of eacbfeveiil Houfe,. ib*
next thing yon do lay down the depth of
each Hosfe, and draw Lines- in the famt
inaaaer as jfou &t thofe ia tbe i^ and
. -, fludour

The Toung Survejors Guide* 109
Aiadow ihetn alfo aa you fee , that thejp
may reprefent the Gtound-plat of. a Houfe.
. ■ When you come to protraft (he Courtj
lay your Eyc-drau^t before you. Mid draw
(he beiidtng and turning according to difcK-
tion, laying down the mcafure or each fevt'
ral Houfe that is therein, as you did in iha
Streets {..you tpuft-alfo protradt the Yard^
6r Gardeus'that are t^hind the Houff s ^ with
the turnings and windingt thereof accord^
ioely as you lake them.

Mjte^ That when you lalce ibe Groorid*
plot of any( hurch, youmuft be very exai^
in raking the ButtrelT^s, and the Steepis,
^demy one of the Palais, and protract
or lay tfieai down in t^ fame foim and mea*
Cire as you found ihetn I^jnding, and |ha^
dour them very deep , that they may b4
known to be Churches.

You mull , Itkewife ufe the like txs&ntlt
in meafuring and protia^ing HjJIi, Tnns of
Court, Celledget, an4',aU eminent Hoiifett
and Ihadow jdum acceidin^ly. . ,

2IO The Toung Survey's GukJe.

^■■^ ^ Comtries^ - sK jdr^e^ TraSi
■'of Land.

tE

(reared gf Un^ftier^) alr'^arfy 'i' arid ttlflfe*
/farii, W^pbrtng rtJaf' ihe Ingeijious Sarvejror
cannofbe incapable of ^pnlying it tJ tfiil
fri*rft*cil/dr^ IftUl: tfholty omit this, arfrf

Leai'iltfrwyfhemaiidiniMr ^^ori'ftmiMf
phioij. 'in' oViiet !tb' wh/cfa, 1^ ''lis ^fenil^
the fblfbwtiig Lenimata. ' ' '- ' ' ' "' ;' '
-I. AH faundG are pitipagated almqfl even-
ly,' and are obferved to move 8 nifafur«d
Miltfsjo 37 Secohd*; '' '.' ' '. '

'•'Thfirfe tvell 'kiwwD 'ffom,tWla(^,1iM
moft accurate (5bfervatfori(iafcQOT'''^~*"' ' ■ "
Ihe Velocity of Sounds, which */*'^»-7'r'*
arethpfeof Mr^rn-iflM. * *^-

11. An ordinary Mortar is eafily able to
caft a Projcfiile about a Mile in Perpendi-
^lar Heigih; and the Sound thfreof maj
Be heard near 20 Miles.

The troth of both ihefe Propofitions have
been fufBcIently proved by divers Experi-
meoti made by Mr Wbifion iat, that purpofe.

The Toang Sarve^*^ Guide, ' ' all
III. A. Projeaiie may '6b fiU'd with
Con^ufiibld Matters^: to xAb Fidc ai fi>ont
as difcba^'d^!: ^d icDndnqe hmtiiDg itiUt
it comestQ-fltt.GrtJuijd.' ■ ■ \\'.r. .■ [i i^

Tbii ^11: that 'deaS. innRockett, Bomb(r»'
and Mortflra, do vnyMeW Knbur, and k
found~ to be due npon Tryal.

. lyj'Firr,' orLiglic abontis billc higtrl

will:i' bt \rifiJ?t'iil'»he-JJIrght': ihae, *hen«

the AsT ii tolrrab^xidai abodr,7ta 'Miles* >0

This alfo harh bee n made tn anifeft 1^

many iRpkrTnwnU ihade on puipoTit i

' Tir&I^'iw ofthe,PrMem. ■■■_

Let it jShelL^I^ wil^ali e Fite^ fi»D «i

difchii^^, ' aid Jconttnae ^itfnifi ^ill it
comes to 'rfrt Grqund/be ftot'j*! sCndicil-
larly at)op^ a Mtle higlfi otK pf a Mortar al
any conrrmcnt place in' a -clear Night j
and this Diicharge will by th» 3eaif DSi *^^
Interval of t^e Fla^ and Boian^; gi?g the
DiRance and ^Besritrg of an O^^.r^tr'tcithin
the Hearing ^iid Sight .thereof; affording to
the foregoing Lemmata. ' -.

. - Example ^ ' '.^ :

F^g. -A.-' t.ft 'rhe^Beaiiog oF'ISh^ dif-.
charg'd oat of a Mortar at C, and alfo the
Inrlrval'iof Ibe fM-«nf SaMtt thereof be

obfuv^d ■■ bf r^tSala^6iA to' wA E)K>'0;i
H.I.D.

313 The Toung Surveyor's Guide.
H;I.D. placn within 30 Miles nmnd C, who
muft be fumiOird with an InflninKnt ta'
mtafure Angleti f(»r taking the Bearing of
the fhell i and a Thread 39,2 Inches long,
with s Plummet fafien'd' to one end, which
being fufpended by the other end to a Pin,or
Kail, and made to fwing, will vilMvte feconda
by which (he Inferral betwem the Ftafh and
Sound may be nicely meafuied, and let thtir
Ot&ivatioos be aa foUova.

i

1

I'll

■ ■§'

lit-

'fe-.

14 1

Is*'?

Miles.

D.

a i .

s.e: n

14

A.

.,'74

1?

16

e.,

5St

12

E.

835-

S.\ir.4o

iS

F.

Jl

90

11 '

I.

J!t

N.E. 5

12

H

78 r

. !o

17

S

«9.±

aW.Sa

, '! -

Tftpmtraa which , trough tfct'
fam C, i)t>« tin Ucitdno N. S. and lay

off

The Toung ^irveyor's Guidi, 3 1 j
cfftheAngl«iNCD.3',NCA. 5o%NCG.
-^7',(romlheNonhtowardsihe Weft. Thf
AngtesNCE^o°,NCF.£>o\(rom theNorth to-
wards thellaft.Tbe Angles SCI. «'^CH 50*',
liom (he South towards the Weft, Laph
Lay off the Angle SCB 6o'' from thfc
South.towards ihe Eaft. Then fet off their
^tflanai ftom (h« Mortar 3t C m%. DG -=.
-i4»i, A C — 16 m. iS'c. actordiflg to the
•Obfervaiions. So will you have an eiafl
Map of ihe place A.aC.UE.'F.G.H.L, and
Ihe ScitiMttion of the Villages about each
Station tn^y be eafily taken by the Oi^rvec
there.0f after the common method td takiiw
onacainble Diftancea.

COkkOL^RTt. .

t U each Obferver were to let off a
Rocket at his own Sration, and rdk« the
mutual Beartog, of eafh others it woud be a

freat Check to any Error that could pofli-
ly happen.

II. If a great Gun were difcharg'd near
Ihe Mortar, and the Sound ttweof uied in-
ftr'ad of that of theMortar^ it would be beard
much further, and cooTequefUlr a mndi-
larger Traa of Land might be torreyed at
once.

•14 72v Tonne Survgyor^j GuiJu

A teaij vaj to fnd a trte MeridiattUne hy \hf
PeltSur. ■ .

The rigbt Afoenfion of the Pole Star fqi

this Year (171^ '• ?7 Minutes of Tioiej'
-and it increafes sne Minute 16 Secondiere-

Sten Years : Therefore having at any timt
is Stir's Right Afcc^Mi; and the Ri^-
'A&ennon t)f the Sun both in TtnW, if 70a
firi^rad thelM(# ffom the^onAer,- adding
54 Hours to the Right Afcfenfion of the
. i'ule-Star, ■ «1ien it iff left than the Sun's
{he Rcmaindervrillbethe rime of the $ftif\
coming to the Meridian^ at-whidi time
hang tip two Pendulums between your Eye
and the Pqlet'lSbiv -iiid a Right*htie drawn
through them, will be. a true Meridian-
iirie^ •! 1 :■•■'■. ■■ ;' ■ ' ,

in the Snrvey jufl now treated of,' yoa
aiiay nfe ihe -fighh of -a good CircumfereD-
tor, loi^aop MhsrSHrre^inglnftiaihrtit,' ha-
ving one of the fights long ■ enobgh ta
lake inf*iPblefltar: ''' ':':■! ■
■ ' If you ■ wt«*d kmfr, what -'Angle the
£oie*Star mak&s' with the' true Meridian ^
atiwbertimw, the fallowing Table will J
ibdr- -:■... :-■.'. ...y. i . •"

Sideral

Coo^ik \

' The Toung Survefor's Gniie. i rj

merlatmitctftm fKirtkWui*ti

mjidnci'frm/f.

m>2

.i5i»M^fof'o(f. .

Uttni

."'2

1?

O- OO-

'V

6,

5 , 41 f

T

;

o 30 T

't '

3 38-

11

I

I oo 4-

J

7-

i tl

T

X

I 29 TT

t

T

3 20 ■!■

»tf

■''±

'4-'

8.'

*■'; "^.''H

:|

1 pi

-«3; ■26 1' ■■'

"4

ft

■* 5*4^
■J .■ 5I..V

''!

'. 'S'»!i ••}!"■

9

1

■■ j'od-^ -^

■^

J.

r 9 ?■

i

4

• '3 ■!« i- •

2

io

'', "■■'"',■.■,

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■./a;

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't.'t

i.:i'.„V>l

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:r^,'J.,J^ = i^-!K:^H,j,i

t-jj'ioob--""

.■.■-.•■..■\i-ir. 'J tir,(R ,•.*, «tM

Ii6 The Touttg Survgrt>r*s Gvide,

the Names of fuch Colours at are necef- •

faryjor the Wapnng of Maj>s, Charts,

! or rtofs^ with the manner how to

tender and ufe the fdtne upon Velom^,

- . Prf^w (IT Parebmera*

IT .ii not : canT«nient for ■ Siwveypr
when be htth~ drawtt the dianght of i i
Maonor, $nd rrdutcd it to bis thtended j
bignefi, to repair to a Paiotft to finiOi hit *
worfc» the thing itfelf bring"' rety commeUT *
fidblfy and eaue to be atrained : And be>
lides B Painter is not to be fouDd ifi-eve-
Tj Cwntr J, nor if every fainter fumiSted 4
with Q>i°uri futin^f for ibdi a purpore, thejr
far itwmoft part ^n g mor i gr o f i aod-or''
dinary Colours. Now for the benefit of I
fiH-h who defire to ezerrife themfelres in |
tfiiiVind of prafiicr, I have addedthelc ne> j
ceffary dirctSiam following.

Horn to maJu GnmVater.

Take Gun Arabicl: what qaantity joa
plea&« of the whireft and cleareft you can
gel, which hruife into fmall piecei^ and tie
them up loofcly in a fine linnen Rag, then
take of the cleareft Water you can get, and
pat it into 8 clean veflel, as a poringer, (oc
itich like) then hang youi Qoath ia wluch
you

The Toung Surveyor's Guide, 217
yon put your Gum into this Water, letting it
haDg rill all the Gum be dinblved^ then when
TPa ii^our Fingers into this Watefj if you
'£nd thnllk to ftick together, as if they were
"glewred, ybnr Watcrii too fliffof the Gum^
-which you may remedy by putting thereto
more fair Water, aod if you find it too weak,
you nuv add more Gam } with this Water
moH Coloun are to be tempered.

How to rnait Mlum-Water.

Take a Pound of Allum, and beat it to
Pofrder, then take a Gallon of clean Water,
and fet it on a Fire, letting it bail till all the
Allum be melted, then take it off the Fire,
and when it is cold you may put it into a
Teflel and keep it for your ufe : With Ibit
Water, if you wet your Paper before you
lay on yotir Colours, it will keep them from
finking into the Pap^r, and wilt alfo add a
Lufire lod Beauty to die Colours laid diece-

The Names offuchColowsti «re neceWaryfor th»
^afiitigofJ^pSy Ptah, orCbarti.

REDS.

ftiAxms.

BLEWS.

Vimilliai.

Owubeme.

Sice,
iidifo.

Sad Lai

Orpimitt, i,e.

Vaster:

w-

jhjnick

Ulmofe.
,L^«d

L

Braitl}ei

■^2 1 8 T'/jtf Toung Surveyot'sG^Ue.
REDS YELLOftS BLEWS GKEiNS.
Braxik. ' M-iftkot .UltTamerme Bic^,
Turj7foUe. S4''o». the btJlBIue.Stp Green.
Indian Caht. Vertdegrea^,

Cm mm the Verditure^

hejl Red.
Scat la Flpch

B L ACK S, WHITES. BROWNS.

Lamp-Bhck, White S^amjb-Brown.

Printers-Bhck. Le^d in Umber.

Ivory iShaxmg fijkei . TfoodSoote.

Hjfti-Hom T bw«t,. SIndesofGiem

indiJK-Ink. WaUnutt.

If. B. Colours made from Vigitables
fades the fooneft.

Being thus provided of ihefe feveral Co-
lours here named, which yo.ii may have ia
divers places in hpnAov, as alfo of 9 Grijod-
ing-S'one and Multer, which any- Mafoo
in London win furniOi jou wiih, alfo di-
vers Pencils of feveral fizes , and Gally-porf,
Gar-GUiTes, or Horfe-Mufcle-fhells, to put
your Colours In when they aie ground and
tempered, you are then ready at any time
to m^ke ufe of them, and now- will 1 Oiew
you how aU the^ forementioned Coloois-arc
Co be groimd and tetp£*^ea»

Of

The Toung Surveyor's Guide, 3 1^

Of the orderv'g of Oihurs.

■ Of t'hefe Colours before mentioned, fome
are to be Groimd fome Ifafitd^ ibme only
Steeptd or Diffohed, others to be Boyled, a&i
Tome to be Burtitj and then Ground.

1. Hw atiy Cohnrh to be Gromd.

Take what Quantity of any Colour yt*
pleafe, that ia to be Grotrnd, and lay it up-
on jour Grhivig-fime, being clean, as alfo
your ^»/fcr, then with yoai Muller bruiflt
the Colour, if it be lompiOi, and when it
is reafmable fmall or fine, put fome fair
Vat*r to it, and with your MuUer grind the
Colour and Tf^'ater together till it be very
fine ; then with a Kuife or piece of (hin
Latahan-hont, being clean, take it off iiom
th&Sfone, and put it into a Shell, and when
it is dry you may take it out of the Shell,
and keep it for yoor ufe.

The Ctlwrt to ^eGratoti are,

rerm'tSm^Lake, Indigo^ MaJHcot^ WUto-teaii

In Grinding of your Colours put not too
much Water to them upon the Stone, for
they ought to be gtound Stiff, like weak
Pafte, 01 Pap.

La 3. Bern

>30 The'Tottng Sun)eyor*s Gmdsi

2. Haw Colourt- mt to be Wnfisi,

■Take a goo^Qpantirj of the Colour wfncfa
you intend to i^*^; and put it into a ^afm^
poaring to it a good Q>ian(ity rf /jir Wattr^
and ftir the Colour and tbe Watst oftoi toge-
ther, and then you will fee a great deal of
filth IVim at the. top of the ^''ater i when the
£xi]»ur ii fettled to the bottom of the fiifun^
pour away that Water gentlj into anoHter
VtHel or Bafob, and pour oiorciair Wat^
to (he Colour, then ftir the Colour and thrt
ffflh Water together, Md when the Coloox
» fettled, pour away (hat fecond -Water to
the foimer, and (b put'a (bird and fonrtfa
Water, ftirring it often till the Water come
from the Colour without filth, then is joat
Colour Walhed : But before '*ftxx take tb*
Colour out of the Veflel, lay it with yoor
Hand very thin about the fide »of the VrfTel,
snd when it ii dry, fome of it will fall to
the bottom, which put upon a (heet of Papeii,
whidi will be good Colour s but the Remain-
der, which flicks to the.fidei oF the'Bafon,
is befl of all, which with a Feather Arike
off the fides of the^VeiTel, for it will be
•finer than any Flour.

Tie Colpurx to U Wafbti art^

'Seffet. -. Sice Orpiment

Kid-Ltai Verdittr SffmJb^Brvm-

- There

Tk* Toung StdTvejor's GiuJci 221

TiKfe cr other Colours rhus w^ed. yoU

may refeive in white Paprr trre fromDtjft,

and make ule of them as you have occa^on.

3. How CoJotns are to hs Steeped.

- This is only to pnt the Cahm into fome'
kind of Liquor^ and there to diiToIve ; ^onl^
io cold Liqaora, others xx\)on the Fire .

The Cohan to be ^:eped hi cold Liquors are.

TeUov-Berries,

Sip-G e:v.
' Litmofe.

Qam Bilge.

Safron. .

Indian Caket.

%

The Colours to he Jheped or billed are,

Frendf-Verd^reafe. Turvfoil

Brazil JfoodSoot.^
Le^vooi.

Rhtdes of WaS-nut!,

Theft Colonrs when fteeped at boiled. are
to be kept clofe in Glajfes, till you hat'e
gccafion to ufe them.

4. Hon' Cohan are to helurytid,

.Some nfe only to pnt a Lump of Colour

into a Red-hot place of the Fire, and there

Jet it lye till it be thoroughly burnt ^ lut this

L 3 is

if both wafteful and floveoly. Tbe befi v<I)l
V tbii.

Tike a Quantity of your Colovr^zud pnC
it into a dean Crucible, putting thereto fooie
Pair witer^ then cover ihe Ciacibk with CTa/,
arid fet it into a hot place of the Fire, let*
ting :' t there continue till the Oucible be Red-
hot, then take it out, tnd when tc it cold
^ou any take out the CoIunt^ aod gond
If as ii before taugh\ .

Tbt Colours to he hwtttare^

Spmi^'Brovn. frinters-hUck. luory.
Ifmber. Lamp-bhck. ffartt^ont

Or anj other grojt and foul ColoMr.

Having ihewed you the way how to QrW,
Wjp, Steeps Boilj and Ban your dlourt^ 1
will Ihew you now

y. How to timper^our Cohurti,

Tirfi, Such Colours as are gromti witV
Fair-water, take a fmall (Quantity thereof,
and put it into a MifiUpell, putting there-
to fome Gum mater^ and the Cvlovr in a fhort
timewill be molified ; then with your Finger
(being very clsan) bruife (he Cohvr againfl
the Shei, tiil you find no jbtott undifTolved^
then with a clean ^mcil ftroak down the
Cdoni towards the bottom of the SbtJl, and

Ths Thung Surveyor*! Guide, 225 ■
it is fit fta afe ; but if it be too thick, add
more Gum-water to ir. .

Stich Colntgrs as tnV^afied^ yoH m'jft
t«(Apei in a SheS tiHItli Gva water^ in llje fame
niBRnft as yof did tbofe tb«t were Gtoundi
• Such Colotira is are' Steeped, the Liquor
osly o[ thbm is to be uTed, witham any
Addition.

Of the fivsral Simple Cohtm^ how toor^erthm,
, without any mixtures,

I. Of R€ DS,

Carmine, beirig tempered with wtafe Gum-
water makes the beft of Reds.

yermilHvn ,htiH^Gioand and temperea with
GUpi-Watrr,tiiakes i detpRei otSctriHC^omi

Lahy Ground aod Tempered with Gum-
water, makei a deep Pink or Bloom Colour.

Red t^iJ, Wafiedy is a braW Orient, Co-
lour, between a Red and an Orarge Colour.,
. Se^r, Wathed, and tempered with Gum-
wster, differs not much in Colour from
LakBy bat it will foon fade and grow H^ter,
W being tempered with Brtoatwjter it will '
he more deep.

Br*iJl, The ShJvifigr or Crtn^rigi ihere-
i»f being bbiled in Viatgar and fmaM Beer (or
fail-water) in an Earthen Vefiel, with fome
powditai JSnm pnt therein to heighten the
Cofoii?, Slakes an exceUeHt Fini- or ^ight Vidht
CtieWir When you flrain the Ihiquot from
1^4 the

3^4 The Toung Surveyor's Guide*
the dregs of the Brazil^ add tbcceto fome
Gum-Arabirk to bind it.

Tun^ail It is made of Lmm Rttgt ifed*
which being put into a iSiiiKn- or the ])ke>
with Coait Vinegar, and ftt upon a Chaiiag'
diftl of Coals, the Rsigi fqueczed into th*
TWPfar, with fome Gam to bind it, makes
a good Colour to fliadow all TeUowt with.

ht^ati Okei. . Ufe them as yoa do Tant-
foil^ and they make a good Rei-trmfpareitt
Colour : loto the Ligaor put fome Gum to
bind it.

ScarUtPhch, (which ii bought at the
Cloatb- Workers,) boiled gentlj in Fair-water
for about $ Hours, putting a fpoooful of
Soag-Lett to bring out the Colour { makes
an excellent Traufparaa - Red , or Scarht
Colour.

2. 0/ TELLOirs.

Gtanhoi^e^ Steeped in Fair water onlf,
tnakes the moft excellent, and moft tranf-
pa^ent TeBov Cohur : It is of that Nature,
that it will admit of no mixture.

Telloa-Berrhs, Steeped in Fair-vater and
a little pnwder of ASwn added tbertto
(or fteeped in Allnm -water) makes a very
good and Tra^ffparent Tellow.

Oipimstit^ Wafhed and tempered with

Gum-water, makes an Orieut or GofdrColoMr,

tbore

7i« Toung Survej/or's Guide, 523
there are feveral degrees of it, fome more
Red, and others more JeBov.

Mafiictt^ Ground and tempered with
Gum-Hrater, makes a good, but no Trarf-
parent Tellowi:

SafroHy Steeped in Fair-water all night,
malces an exciellent Traofparent Gold Cc-
low.

3. Of BL UB S.

UUramerine^ B^ing tempered with a weak
Gum-water makes the befl Blue.

Bicty WaOied and tempered with Gum-
water, is an eicellent Blue, but not tran-
iparent, and there are feveral foits of it,
tome lighter fome fadd^.

itd^Oj Ground and tempered with Gum-
water, makes a deep ££uf, and it fit to
fliadow all other Bluet.

VerdUer, Wafhed and tempered with Gum-
water, is a good Blue^ but not tranfparent/

XAtmofe^ Cat it in fmall llicea, and fteep id
in a weak Water, made of Gum-Bl»ck, for
the fpace of a day or more, and you will
have a trmfparevt Blue.

Logwood, Boiled in all refpe^ m Brazil^
makes an excellent VioUt or Purgk-Cokv,

4.

aatf" Tie Totm^ Sttrvejior*i Gukk't
4^ Of GREENS.

Bite, Waftied snd tmtppred with Gtam*
water, makei a good, but no (ranfparent
Orttn.

Sap'Orem^ Stcfp'd in Fiir-wtiter, and t lit-
tle I'owder of Allutn added ihertto^ makea
a good (rr^BM to Ihadow of damaf^ withat.

Veriitvre^ WaOied and tempered with
Gum-water^ makes a Green, noftraofpatent^ ■

Haifa pound of Frcncb^^rHgreafe, boHed
with a Qpart of Fair-wdt«r', putting irt
in Ounce of Jriol to Wing OBt the Colour,
makei an excelleAi Tranfparcnt Orem U.-
fliniog to BIwt.

N. B. This Colour muft fee boiled very
gently for aboQt five Honn, then take it
off the Fire and let it fettle all Kight,
and the next Mornine pwix off the cleat
part.

y. OfBLJCKS.

hiJi/K'hik^ Grotmd and tempered wird
a weak Gum-water, it the beft Black fot
OiiidDwing deeppi' Bbih.

Lamp-btaiky Prifiters-hljck, Tbory^ Harll-
Hom Shavings, b?ing Barnt, Ground, and
Tempered with Gum-water, are all good
Blacks..

6..

The Tmng Surveyors Gmde. a a ;r

e. Of WHITES.

WTjite-t^eai^ Gronnd and tempered with
Gum-water, ii the befl V^hiie.

7. O/RROJTNS. "

Spam^-Brown^ Burnf, ground and tem-
pered with Guoi-warer, nuk<;i a Reddifi-
S^owtt or Liver-Cehur..

Umber ^ Burnt, ground, and tempered
wkh Gum-water, makes a g^nd B^a-
Co/oar, and ia good to fiadom upuii
Go!d^

M^ooi-S*ot^ or Raist of Tf^all-mtt, K-^iled
in Fair-water, and flrained, and fomeGum-
Arabick put into the Liquor, to bind it, either
of them makes a moll excellent Colour
£» tp e:^refa High-ways, Laavt, £?'&.

Of Mixture of Colours.

fj\' the fore-mentioned Colo'jri that we-
have hitherto treated of, are fuch as arc
iimply of themfelves, without any mizf
tare, of which infinite may be compounded;
nay, altnoft what you wit). But for- our
purpofe the moft iranfparent Colours are
the Principal, fox this our purpofe of Co-
louring of Plots. Of which Brazil and
Z/fsvood Water. Carmine, Indian-Cakes. Tum^
foil.

a 2 8 The Toung Surw^er*} Guide,

foil^ Ultramnjne , Gvmbooge ^ TeUew-berriet^-
SjffrcH^ Litmofey S'p-Green , Frmch'Verdigreaft^
Vtiod-Soot and Wabml-bvfii, are the prin-
cipal, and of tbefe feversl others may be .
compounded.

■ For G REE N.

Veriigreafe-water , and TeSom-berry-watery ,
makes an excellent tranfparent Grem^ either
fadder, or lighter, according to tht Quan-
tity that you take of either.

For BLUB.

Utmofc-Vater ^ 'fo which add TelIow4>erry'
pater^ and you have a fad Grem.

For OS AN.GE Cohtir..

BraxiUgater and TsBoV'btny-wattr,

%■ In^nite Colours, I Tay, may^be made
oF theft, which may better be found out by
pradice d)8n by many words : And there-
fore Domi- will fhow you what Colours
do fhadow one another.

Cimcemittg Shaiowirg.

All light Cdlouri are fhadowed with

Colours of ibeir fame Nature but more

fad.

■

The Tmng Swvejmr's Guide, jjf
fad , for which take thefe BricF Di-
redions.

Virmmn, -1

tLthfitSimijh-inim

Vtiiitir mi

Bk,.
Gmibxt' ml

W«».

.

VmbtryiAltai-Uai
or VaiMim.

Teiou-heniei.

JUi-LeaJ,

Is

Lah,tir Spmifi^om^

Mafihote^

Sha-

E,iO,pmM,

Sfmajt^an.

SurM U«ber i:b

ed

Brnil-vxteT.

Vmba;

with

UnU,n S„,t,

RofntniSra-

^anifi-brown ^ mixei

Jai, Re.

with Brttzil^waler..

Veriipiaft,

hUfo md n/fcu-fci-
ri water mixei,

'Vmkr

fVoolSmt mi

rVaUuts, .

^

VMceming the laying on of jow G)-
* hurt*

For the Ia]nng oa 61 yoac Colours, 70a
muft provide jour felf of Pencili tA feveral
Hzes, bigger and lefl«r, and if jrou will be
curious, you oi^bt to have a gr^at and a
fmall to each refpei^ve Colour, if net you
mtift always have by you a difli of fair-
water, in which yon muA .fwtll or cteanfe
your Fenrily wiping it with with a Cleaa,
IJaen

13 9 The Toimg Surv^or^s Ouide.
Linen Cbath, before ^ou put it into ano*
ther Colour.

For yonr P*ncilf, you may chnfe,' in
your buying, tbofe that are good id this
manner ; See that they be fulleft mit to
the Quill, dertwiding or leffening into a
fmall room am} ibarp point, which yoa
may produce by putting of the Hati mro
vour Mouth, and drawing it through yoar
'^pa once or twice, then may yon fee what
it is, and if yoo find any eitravagant
Hairs, /inge them off by a Candle's Flame.

- Being thes provided with Colours and
Pencils, if you would lay any CoIoot a-
fiout the fidges of any part or piece of
Ground in a Plot \ as fuppofe you would
inclofe a Field in a Plor with fellow j
with your Pencil take of Gumbooge or
Tellowr-berrie*, a very fmall Qosnti^yi ^d
on the infide of the clack-L°ad-line, draw
the Colour along oT an equal breadth ( ai
mar at jou.can) iiom. the L'ne, broader or
narrower, according U your ^^V is in
bigncfs (wt daidfhig yoar rieli *aSover vttb
Jomr Cnlowr^ as I bavi feen fame, otherwife
good tbitgij by this plaftering way ( at I
may call it) moH nororioufly abufed. Then
having gone round your Field in this
manner with your Colour, wet yonr Pen-
cil in your Month, or have a fmall Qtun-
tity

'The Toung Surveyor* s'Guide» 250
•tily of Water by you to dip it in, and
IHike along the infide of the Coloured Line,
bringing it more down roumrda the Center of
the Field ; and this will fweeten your Co-
' lour, and ~m3l:e it fhow as if it loft itlelf by
degrees, to the very Colour of your. Paper
or Parchment.: And this coqrfe is to be
taken not only for Tellowt but for all other
ColcuTi. Then laflly with a Pm (if you

! cannot handle a fmall Pencil handleinely-
asd evenly) tak--' (btae of that Colour which
> fhadoweth that Colour you coloured your
I Field with, and go over your Black-Lead
. Line only,fo fhall your Field fee fimfli'
i <d.

ArtiJ' in this msnnep nity yott do a Hnn^
\ dred Fields in one Plot, of divers Colours:
' , only obleive this, that as near as you can,
you colour not two Fields adjoyning one to
i riw ptber- both of tHe*fsme Colour^ but of
different: and therefore it will be conveni-
ent to underftand what Coibura do fet one
another ofT befl, and as new as you can to lay
I Clofea. adjoyning one to another, of two fuclj
^Colouri, that one Shadow may ferve both.

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